Creaking when braking and stopping?

Better suspect is a suspension bushing. To work on the brakes, you have to jack up that corner of the car, and that lets the suspension hang down, twisting the rubber bushings to their limit, meaning further than during normal driving. That excessive twisting can grind rust loose that doesn't come back for a couple of days. To prove if I'm on the right track, when the noise comes back next time, jack the front end up for a few minutes, but don't bother removing the wheel. Just set it back down and see if the noise is gone.

Another clue is you may be able to make the noise occur by bouncing the corner of the car. If that works, the brakes aren't involved with the noise.

Regardless if that leads to anything, a good tool to find the cause of an elusive noise is called the "Chassis Ear". There are a few different models including some with wireless microphones. I have the oldest model that uses six wired microphones. You clip them to suspect points, run the wires inside to a switch box, and you wear a set of headphones while driving. By switching between the microphones and by moving them around, you can zero in on the source of the noise.

I found the tool on eBay for around $200.00. Don't know what the cost is for the models with wireless microphones. You might find this at an auto parts store that rents or borrows tools.

Let me know what you find.

Rats. I'd pursue the Chassis Ear next. I forgot to mention, as you switch from one microphone to the next, one will make you think you're getting close, but when you switch to one that's on the noise source, it will be real obvious. You can clip one to the brake caliper, but you'll have to be careful when running the wires that they don't get caught in anything rotating. I like to tie up the wires so if a microphone pops off, it won't drag on the ground.

Don't forget to try just jacking the front end up, then setting it back down, then let me know what happens.

Dandy. I'm here every day, normally in the early to late evenings. Will wait to hear some good news.

Do you mean temporarily, or will the noise come back?

I see you lubed the backs of the pads where they contact the piston and caliper's fingers. Another place that needs lube is where the pads sit on their mounting surfaces. Lube on those points is more to reduce wear than to prevent noise, but if the rotor becomes just slightly warped, as most new ones do once, that makes the caliper and pads walk back and forth a little once per wheel revolution. If grooves wear into the pads' mounting surfaces, they can make a clicking noise when the brakes are applied. The pads are held tightly against one surface as they shift left and right a little and go into and out of those grooves.
When those grooves aren't worn in yet, a low growl can occur during braking.

One clue to look for is how the squeal occurs. The first thing I thought of was a worn rubber bushing. That can make a horrendous squeak, but only while the front of the vehicle is in motion moving downward, just at the start of the braking cycle. After that, the noise will only occur some more if the tire hits a bump or pothole. During a long stop, the squeak will only occur at the start of braking.

If the squeak remains constant as long as the vehicle is still moving, it has to be caused by something that is rotating. The frustrating part is that noise can be much too low to hear directly, but if it gets transmitted into the caliper, that mass can really amplify it to the point it's very easy to hear. That's actually why we put special high-temperature brake grease on the backs of pads. Disc brake pads a going to vibrate, period. There's nothing we can do to stop that. The grease allows the pads to vibrate, or slide back and forth against the piston and caliper fingers without transmitting the noise into the caliper.

A problem every brake system specialist has run into more than once is a bent backing plate, or splash shield. It should have a good 1/8" clearance from the edge of the rotor. If that clearance is too small, it can cause a noise only during braking due to the number of different forces acting on the caliper, rotor, and wheel bearing. You'd find this pretty quickly with the Chassis Ear. Sometimes there's a telltale shiny ring worn onto the backside of the rotor where it was touching the splash shield, but we usually see that only after the actual cause is found.

Another clue that points to a suspension bushing is the noise seems to always disappear for a few days right after any brake service is performed. The only thing that occurs consistently is that corner of the vehicle has to be jacked up, allowing the suspension to hang down and stretch the bushings. Same is true of ball joints. The extended travel redistributes the grease, making the squeaking go away for a while. A squeaking ball joint will occur at the same times as a rubber bushing would squeak. You can eliminate those as suspects if the noise is constant during braking.

A creaking noise that threw me for a loop a few years ago was caused by a stamped metal wheel cover. It could be heard occurring very lightly while walking slowly alongside the moving car, but the driver couldn't hear it until braking occurred. That put more weight on the front wheels, and the braking forces caused the wheel to flex more than normal. A very light film of axle grease around the wheel on the wheel cover contact points solved that. The creaking sounded exactly like a worn rubber bushing, except it was constant during braking until the car stopped moving.

The last thing I can think of used to effect mostly GM front-wheel-drive cars, but it could apply to any brand. Typically, right after a normal front brake job, a grinding noise would develop, but mainly while turning, and not so much from braking. It was found the rotors were flexing under the wheel and lug nuts, even though everything was fine and the lug nuts were torqued to specs. The noise was solved by placing a light coating of axle grease on the hub where the center hole of the rotor sits. That allowed the flexing to occur without creating that grinding or crunching noise. Now it's standard practice to put a little lube on the hub whenever the rotor is reinstalled. I like to use Spray White Lube. That's a lithium-based grease, but be careful to not allow any overspray to get on the rotor's or pads' friction surfaces. I consider this more of a preventive maintenance for the one out of a hundred vehicles that might develop that noise.

Have you given any thought to locating a Chassis Ear? This is exactly what they were designed for. Instead of buying one on eBay, you might be able to borrow one from an auto parts store. In my city, they make you buy it, but you get a full refund when you return it. If you choose to keep it, you still return it, then they give or order you a brand new one.

Would it be possible to upload a video clip with the noise occurring?

I'll believe that after you post a follow-up that it solved the noise. Outer CV joints make a clicking noise when they're worn, most commonly when turning and backing up. Worn inner CV joints can cause an elusive steering wheel oscillation when under load or moderate acceleration, but they don't cause noises. I guess anything is possible, but you might consider getting a second opinion.

When I work on an unfamiliar vehicle, I do just one side at a time so I have the other one for reference when my mind falters and I forget. Before you take that other side apart, check out this drawing.

When lubricating parts stops a noise for a little while, that's a clue, but not a fix. It does suggest you found the right cause. If you look on Rock Auto or any auto parts store, the caliper parts are available in complete kits. Installing one of those repair kits might put an end to this aggravation.