After taking off the front access panel and removing the pump, I was able to determine that the pump really was worn out. I then started looking online for replacements. AppliancePartsPros.com seemed like they had a reasonable price and claimed fast shipping, so I ordered one from them.
I placed my order around 4:30 pm on a Friday and was amazed when Fed ex delivered my new pump the next morning around 10:00 am.
The actual removal and installation of the pump only took about 15 minutes, while moving my washer out on the porch to work on it took about 30 minutes.