I'm sure you've already done some research, but they're not terribly hard to rebuild. I saw a guy w/ ZERO experience rebuild one on his workbench for a project. He had a transmission tech come and check his work every so often and it passed muster.
I had the benefit of a good friend who built transmissions for drag racing in his garage. He didn't have any real specialty tools (maybe a couple) but it was all very basic.
My guess based on the slippage in first gear is that you've got some broken/worn bands or a servo/solenoid is stuck. It could be the converter, but that usually impacts all points of the driving range. Meaning, everything is slushy.
You could try some Lucas Transmission Fix . I have had great success with that stuff in milking an old transmission along. I had a rear seal in a transmission completely gone. It would slip and carry on, but I put this stuff in and I ran that way for 2-3 years! It's cheap enough to try it out, IMO.
You'll definitely want to take a look at rebuilding that transmission though. It's telling you it's upset lol.