The project is finished. The answer to my question is that yes, you can repair an inducer motor (at least my motor) instead of replace it. But due to my own carelessness I didn't. Here is what I did right, and what I did wrong.
Following advice here I decided to replace the inducer motor myself, so I called the repairman to cancel and he asked me to pay his normal $150 service call fee for the initial diagnosis, so I will. Better than paying $850 for the replacement.
I bought a new inducer motor from Amazon using Prime for $88 and it came the next day. It took me a while to find a gasket for a reasonable price, but I finally found one for $12 (part and shipping) that came in two days.
I had already taken out the old motor and thought about taking it apart to see what bearings it had but for some reason did not. More on that later.
Due to various stupid mistakes it took me about 30 minutes to remove the motor, and then three days later, about 30 minutes to replace it. It was a little hard to keep the gasket in place, and it may have slipped out of place. Apart from that the replacement went well.
The new motor is completely silent. I turned the furnace on for a test and almost turned it off again, thinking that the motor wasn't running. Then the flame came on and I looked more closely and saw that the inducer motor was running, but silently.
Then I remembered to take apart the old motor to see how the bearings had failed, and I'm sorry I did. The motor housing came apart easy enough and I found that the motor had ball bearings, not sleeve bearings. The size is the common 608 and you can buy 10 of them from Amazon for $5 (free delivery).
So unless I'm missing something, I could have replaced the bearings for $5 and had a perfectly serviceable motor if only I had looked at the old motor before installing the new one (which I could have returned for free).
Motors don't (normally) wear out, just bearings. The bearing on the furnace side is the one that is noisy. I pulled off the rubber seal and it has no grease at all inside. I greased it, but it still makes noise (a ticking, slightly grinding sound, not a squeal). It's shot, and I'm sure it degraded because of the heat. The outer side bearing looks nice and greasy and sounds perfectly fine.
I ordered the bearings and they arrive tomorrow. I'll have to figure out how to pull the faulty bearing and press the new one back on. I had the tools for that before, but I can't find them now.
I could kick myself. Not just for the wasted money, but for replacing a motor that could easily be repaired with a 50-cent bearing. I'll repair the old motor, but I'm pretty sure I'll never use it again. Too bad the repairman lied about these motors being unrepairable.
Live and learn.