I see.

Is this a water cooled unit? If so, you may have a hard time finding a shop that will rebuild it. If not, a reman. traditional alternator is fairly cheap from the right source. I want to say $150ish?

It's not likely that the alternator issue is causing the trans to free rev, though. That sounds like an internal trans problem. But the alternator may solve multiple other gremlins.

Good luck.