doubt you will find a $1K Tranny rebuild in the LA area. More like $3K. Might still be worth it. Another option would be to buy a rebuilt one and have it installed, or install it yourself.
Just re reread and saw the $1600-2200 estimate. That is a very tough one; as the repair price is reasonable. However here are a couple of general car thoughts. I typically consider 200K to be the end of life for most cars. You start to have major component failure, such as transmissions. If you fix this, what will be the next thing to fail. I certainly have cars that are older than 200K but, I am constantly working on them. What is your replacement going to cost you and are you able to cough that up right now? What is the resale on ol Besty. With a cooked tranny $500(?). Running $4000?
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Also the California cars being rust free is a misnomer. If the car lives near the ocean, within 1 mile or so, it will be a rust bucket. If it live in the mountains, they salt the roads, it will be a rust bucket.