I wish I would have seen this last year. I'm replacing my Caretaker (piece by piece) this year. I did most of this exactly 10 years ago, but this year (or decade), it's turning out to be a little bit more involved.
Based on my experience, I don't think the reason your motor wouldn't come out was because of a rusted shaft. Mine has been working for 10 years in a saltwater pool (and exposed to water that has leaked into the housing multiple times) and while many other parts were rusted, the shaft was not. It was more likely that an o-ring "sheared" and was interfering with it coming out OR it was just a really tight seal in the first place.
I hope you got it fixed for under $4K.