My Saturn 2005 L300 has a little under 38,000.

You should change your transmission fluid every 30,000 miles or so especially if you drive in stop and go conditions.
The Dexron III is what you want to use and the Dexron III/Saturn is no different, probably just what Saturn does when they sell Dexron at dealerships. As for the Dexron VI you cannot use it and it will cause problems. The Dexron III is a good fluid and you are changin at what some would consider and early interval, although I don't as automatic transmisssiioon repair is very costly and the price of a fluid change every 30,000 is nothing compared to $2000.00 or more all at once. If you continue to maintain your car with these types of intervals for ALL the fluids, Anti-Freeze is a big engine killer do it every 2 years, your car will get 200,000 miles before it gives up and needs to be replaced or have major service.
You can use synthetics on the engine oil and I highly reccomend it. However you should use an oil filter made to work with synthetics. Also, don't go way over the 3000 mile oil change interval just because you use synthetic. If you are in stop and go conditions in polluted area your engine will still get the oil dirty and contaminate it and even good sythetic oill can't work well when heavily contaminated. You kind of have to start looking at the oil at 3000 miles and see how dirty it is. Change it when it starts to look dirty and also clean your oil pan very well so when you put your oil in a container you can look in the bottom of the oil drain pan and inspect for small particles of metal. You ahve to get under light or sun light to see them and they are an indicator of engine condition. None means a very healthy engine. Silver colored particles means you are heading towards needing a rebuild. Then finally a brass or copper colored metal particle means you are in need of a rebuild within the near future.
I am always glad to see someone who understnads, ""$10 in maintainence saves $2000.00 in repairs". It is a very true statement.

Anything that says DEXRON III on it is okay. You can double check with the shop but it is simply another name for the same transmission fluid.

When I worked at the saturn dealers we changed the fluid every 50,000 miles as part of the maintance service intervals but by then the fluid is very dark. Because the clutch plates are fibrus meaning as they wear they release fiber material in the fluid that material travels threw out the transmission.I belive that is one of the main reasons for all the issues with the pressure control solenoids on those earlier year L model saturns. As far as the saturn fluid goes I belive it has extra additives over the regular over the counter fluids. The S model fluid from saturn was involved in a bulletin for gmc trucks with shifting issues. It said to use the saturn fluid to correct that issue because it had extra additives the normal fluid didnt.

I would stick with the dex 3 thats all we put in them at the saturn and when we ran out of the saturn fluid we used the regular dex 3. Since I havent been able to get the saturn fluid anymore I have been using the castrol high mileage transmission fluid in my saturns and families saturns.

Forgot to mention always change the filter with the fluid also when you make short trips its harder on the fluid and the transmission. Only mentioned that because you mention the short trips. Yeah I satrted with saturn april of 1993 till they closed the last dealer I worked at in may of 2009.I really miss saturn it was a big part of my life for such a long time iam hear if you need me. If you ask another question and want me to answer it start the question by saying this one is for saturntech9 and they will save it for me. With the launch of our update site makes it alot harder for me to track already answered saturn questions to help out with them.

The funny thing in the case of your car they use that transmission in other gm cars.I think the transmission they dont like is in the S model saturns that only use in saturns. But there super easy to work on and are very predictable when they have issues. Yes iam here for I may not answer right away depending on what's going. On at the time but will. Get back. To you