I *am* starting to think about the capacitor actually. The only thing I'm not sure about is whether the capacitor could cause it to stop running when it was already running, because that did happen yesterday.
I took the motor/fan assembly out today to have a look. Funny thing is when I went in there to start disconnecting it I noticed that the fan will now spin without resistance. Maybe I knocked something loose yesterday when I was messing with it? With a flick of the wrist the fan would spin 3.5 revolutions or so which seems pretty good to me. Smooth and silent without a hint of play.
The motor is a GE made in USA and it doesn't appear to have any lube points so I'm wondering if the sticker is just wrong or if maybe the motor was replaced at some point in the past already.
After cleaning all the dust off it I put it back in and it's running now, warming up the house before we go to bed. HVAC guy is coming in the morning so I'll see what he says. I'd love it if it were just the capacitor. That would be a nice cheap fix and if it's on its last legs we could take our time finding a replacement.