Ignition coil module suspected faulty, can I switch modules around?

Yes, that is a practical option. Generally, what I suggest is to swap the coil to a different cylinder. Then swap the plug to another one as well. Then see where the code shows up next. So, if you start with a P0304, swap the coil to 3 the plug into 2 and now you have a P0302, it's likely the plug. Same with the coil. However, that car uses a single coil to fire two plugs at the same time in a waste spark system. If you get a misfire for one cylinder it should also show for its mate. In this case that would be cylinder 1. As such I would suggest it's not the coil. It can be the wire or plug, but it could also be something internal.

In your case I doubt it's the coil. Why? Because each of the 3 coils fires 2 spark plugs at a time. So, with a P0304 code you would also have a P0301 code if the coil was bad. The coils can be swapped around as long as the plug wires are kept correct. What I like to do to save aggravation is to mark them with white paint markers. On the engine the lowest coil should be cylinders one and four. The center coil is cylinder two and five and the top coil is three and six. The plug wires just need to go to the correct coil.

True, these days if you want to be able to do your own work you need a scan tool. You are lucky in that you have one that doesn't need it for things like brake or steering work or to reset the oil life or to set battery parameters, so the charging system works. But a scan tool that can handle more than just reading codes is still very much needed if you don't want to throw a lot of money away. A good source of information is also very helpful. If you want to learn how to use the new toy I can give you some links. What tool is it? I could look and see what it can do and give you tips on where to find tests and results. Unfortunately, the scan tool world likes to play with things and the OEs don't help when they sue because of someone using the names they call parts. As such you find things like the Forward Control Module, Totally Integrated Power Module, Body Control Module and Generic Electronic Module all being the module that does the same jobs in different makes!

That one is a bit more advanced than a basic code reader. Given the level of diagnostics in your Buick it should be able to handle reading the engine codes, looks like it also has basic explanations as well. Should take the place of the free scans and "helpful advice" the parts stores give you. Pair that with this site and you have some good tools to start. You might look at both Alldata and mitchell1 service information systems. Both are used by shops and dealerships and each offers DIY subscriptions where you get access for one vehicle for a set time. ( https://eautorepair.net/ ) for example is $20 a month, $40 a year or $60 for three years. Alldata is more money and basically the same information. The thing about both sites though is that you can print out the pages Now if you were to get the one month package and use a windows computer that does the print to pdf printing you could have an entire pdf version of the factory service information saved on your computer. Including the codes, tests, and the code setting criteria which can be very helpful. Say you have a P0304 code, you would get a chart like the images attached to give you a testing process to use. Some of the steps in those charts are actually useless because the tests don't really tell you anything useful but they can teach you about the processes. Now if you really want to learn some more interesting ways to really test the various sensors and know after testing if the part is good or not, there is a book available written by Paul Danner (aka Scannerdanner)
https://www.scannerdanner.com/buy-the-book.html that really dig into the various pieces and sensors and how they work and what things really work in testing. Then you can be the one in the family and friends group that folks come to when they have a light on in their vehicles! Then you might decide on a mid-range tool, or even opt to jump in the pools deep end with a pro level scan tool with full bi-directional abilities that can handle every system on 99% of the vehicles around you, something like this one:
https://www.topdon.us/collections/professional-series/products/phoenix-max?variant=44112567271702

Mitchell is the better deal in pricing and yes, they cover pretty much all of the service info you may need. I use 4 different services myself because just like scan tools they each have different features. However, for the DIY that would be very cost prohibitive. Just like buying a pro level scan tool wouldn't be for the average DIY simply because of the cost per use factor. Pauls book is more if you decided to go beyond your vehicle in terms of learning how the various sensors and circuits work. It isn't casual reading but if you decide to go farther it can help.

Sounds like you are going to take my job soon lol. You can always ask for help here, but getting the service information so you can read it yourself can help. Especially if you look up a code and see what things cause it to set. Understanding that can save you time and money.

The codes themselves are nothing more than the computer saying "Hey you I have a bad reading in this part of my system" nothing more. Other than a very few very specific OEM codes, none of them really tell you to replace any parts, although on the newer vehicles they are narrowing it down much better. So, take your car. It shows code P0304. That means it thinks that cylinder 4 isn't doing its job. It can tell that using a few indicators. One is the crank position sensor; it knows that at a certain rpm it should see a set time between each tooth on the reluctor. If a cylinder isn't firing correctly, it sees the wrong time. It also looks at the current and voltage as it fires the coil, again it is programmed to see good or bad. Nothing else.
However, it can't see some things that could cause that code. For a cylinder misfire there are many things that can cause it. A bad coil, a bad plug, a burnt valve, low compression (caused by damage to the bore, piston, piston rings) A bad injector and bad valvetrain components.
You go to the parts store, they are going to tell you, "Change the plugs, OH and we sell them". Didn't help, okay change the coil, will that be cash or charge? Oh, gee that didn't help, probably a bad injector then, you should really change them as a set so they all flow the same, Will that be the left leg or arm today? What, it still has a misfire, Oh I'm sorry, here is the name of a good shop, it must be internal damage and they can handle that.
Now in many instances it doesn't take long for a good tech with experience to diagnose the problem with minimal labor. And in reality, most people could learn those same skills or find a video on how to test the items without a lot of special tools. For instance, low cylinder pressure, get in the car, hold the throttle to the floor and listen, you should hear a steady cadence as the cylinders cycle through. If you hear it turning over with a lope, Like this car around the 4-minute mark.

https://www.youtube.com/watch?v=-YgKpfpr3CM

You know it's an internal problem. That basically tells you the engine needs work. For the external parts (coil, wire, plug) a simple test light can help tell you if there is power to the coil, if there is a timing signal to the coil and if there is spark. There are a lot of fancy tools that can help as well but a simple test light and your own ears can do a lot. And you didn't chase the rabbit...
Now a bad parts store or shop might look at this single cylinder misfire and tell you, OH you need a fuel pump, or you need a new ECM and those will fix it. The average person would likely say OK do it. However, if you think about it a minute you will realize, you have 6 cylinders, that pump supplies fuel to them all, how do you get a single cylinder misfire with a bad pump? Then you need a new ECM? HMM, the coils in your car fire 2 cylinders at the same time, but only one cylinder is misfiring, that means the coil is getting the signal to fire from the ECM, so it's not the ECM. Probably more than you wanted to know but it also gives you an idea of how to gauge a shop or even a parts store.

My general progress is, Scan vehicle. Note all codes. Research those using code setting criteria, wiring diagrams and other info. Then develop a plan of testing the items in question based on what those show.

The DIY versions only allow a single vehicle per subscription. So, you would select a plan for a 98 LeSabre and you would need a different one for a 2005 Mustang. That is one of the drawbacks to the DIY side. The upside is the cost is FAR less than what I pay for access per month, but I have access to all the makes and models they cover, same with Alldata and Identifix access. It's one of the reasons 2CarPros exists. We want to help DIYs and pros with repairs and providing the information to do that is part of it.
I generally point folks at the DIY services when they have a single vehicle and want good information on that vehicle. Unlike some manuals that cover multiple versions the info on those covers only that year, make, model and engine. As an example, Haynes offered a manual for the S10 Trucks that covered from 82 up to 94. They had on the cover that the manual was based on a complete tear down. The BIG catch to that is that in those model years GM used 4 different fuel systems on 9 different engines and 10 different transmissions! So, you are looking at the book trying to remove the plugs from a 151 4 cylinder is much different than on the 4.3 V6. Haynes however covers that with "Others similar"
Are they useful? Somewhat, but not for some of the specific things you might need.
On this site we try to keep things simple and have each question as an individual item to make searching easier. However, P0401 in a 3.8 can be caused by a bad EGR valve, but a more common reason in older engines is carbon build up in the EGR passages. Carbon blocks the ports and low or no flow is the result. They can be cleaned out using a chunk of small cable and a drill. Sort of like a Roto-Rooter.

I would expect the carbon to be the issue. EGR doesn't work all the time, it only flows small amounts most of the time. A partly blocked passage wouldn't set the code, however when the system opened the valve up for more flow and the O2 sensors don't see the change they expect in the exhaust gasses you get the code. Sort of like breathing, if you breath shallow you could breath through a straw, now go out and work hard to where you are gasping for breath that straw is going to be a blockage. I would start by cleaning the passages. I generally do it the hard way, earplugs, safety glasses and disposable coveralls with hood. Then pull the EGR off and get the cable in place and start the engine, start running the cable and let the exhaust blow the crud out of the tubes.
Yes the pricing on most of the service information sites are very high. If I add up the costs of service information, scan tool subscriptions, and training classes it works out to almost $1,000.00 a month, without touching a single vehicle.

I try to avoid doing much cleaning. Instead any seepage or leaks get repaired before it's an issue. Removing carbon is a messy job, these days I don't get a lot of those, it's more doing the valves in GDI engines. Those get walnut blasted and I use a special machine that's part sandblaster and part vacuum.
Yeah it's like many other codes, they can be sneaky. For instance a lean code, it could be a vacuum leak or a bad fuel pump with low pressure. Or it could be excess EGR or in an earlier TBI system a bad injector. Most codes have multiple possibilities. The more modern vehicles have more computer power and more sensors and also have a lot more error codes. Some like BMWs tend to roll off the delivery truck with error codes, usually for really stupid things, like the passenger window went up slow, or the left turn signal is blinking the wrong timing. Those can be fun. Your car is much simpler, I'd try to keep it for another 100K if you can.