Initially I replaced the rear drum bearing assembly. I searched all over for a good how-to video and came across the Appliance Pros tutorial on YouTube. It was by far the easiest to understand with the added bonus that AP had the parts I needed.
I had never done this before, but using the video as my guide I was able to replace the rear bearing assembly in about an hour and a half. It would've taken a little less time if I hadn't had to run to the hardware store for a T25 bit. I also could have used a shorter Phillips head driver for getting to the thermal coupling on the back of the dryer. So, take a quick tool inventory before you start taking things apart. The video will show you what you need.
With the new assembly in place, the screeching ceased but a quieter squeak that had apparently been drowned out by the racket of the old rear bearing remained. All indicators pointed to the front support bearing. During the rear bearing replacement I noticed the front was missing three of the four bearing slides and was really worn out.
Back to the AP site I went and ordered a new front bearing support and four new slides. A few days later I had the parts and was able to replace everything in about 15 minutes. The video tutorial for this job recommends disconnecting several wires when you remove the front dryer panel. I didn't find that to be necessary. I was able to swing the panel away from the dryer like a door and lean it against a wall without removing the wires. Your situation may vary. The only tool I needed was a Phillips head screwdriver. The bearing support and slides all snap into place.
After months of squeaking and screeching, our dryer now goes about its business in the same quiet manner it did when we bought it seven years ago. Thanks AP for helping making it happen.