Using a couple helpful videos, I was able to do the job myself. It will be a while before I can say for certain whether this fixed the problem, but I do notice that the drum isn't squeaking like it used to. That's got to be a good thing!
The video Appliance Parts Pros sent me was very helpful with applying the seal to the drum, but I found another of their videos that more closely matched my particular dryer. This helped me actually take apart the dryer.