Well, it's all working correctly now..
I took the capacitor and blower fan to a great shop I found (Econo Temp, Downers Grove, IL). They were able to test the motor as well, and the bearings were borderline bad, just tight enough to occasionally start and run. I bought a new fan from them, and they let me borrow some tools at their shop to install it into the housing, along with some helpful hints. I've learned a great deal about how furnaces work now.
The original repairman was pretty much useless, as he should have known that the fan would be unreliable and should have made it clear that I should replace it now, especially since it's the middle of winter. Instead, he performed a carbon monoxide test without my approval (I have detectors in three rooms, and just had a test done two months ago during an inspection) and tried to tell me I needed an entire furnace, without even giving me a price. A waste of time and money.
I'm glad I met Econo Temp, as I want to add A/C this summer, and now I have someone I can work with!
Thanks for the help, I find myself looking at this message board more often.