Back in 2006 I removed the TH400 transmission from my Avanti and installed a TH200R4. Although I don't have a step-by-step guide for this, I can give you some info and perhaps answer some questions you may have.
Things you'll need, besides the transmission:
1.Torque converter for the TH200R4 transmission. (i'm assuming you'll want a lock-up torque converter to get the full benefit of this installation)
2. Correct flex plate to mate with the torque converter. (the one you have now may not have the proper mounting holes in it to connect with the torque converter.
3. Dipstick tube and dipstick for TH200R4.
4. Flex plate dust cover for TH200R4 Something like this https://www.tciauto.com/gm-universal-dust-cover.html
5. Correct transmission yoke for TH200R4 (depending on what transmission you have now this may or may not be different)
6. Method of providing for torque converter lock-up. There are several ways of doing this, from a simple toggle switch to electronic devices that sense vehicle speed. I used a pair of vacuum switches and a relay that works quite well. It's a home-made device and I'd be happy to share the details with you if you're interested. Otherwise there are many products available in the after-market that work ok too. Take a look through a Jeg's or Summit Racing catalog or at www.tciauto.com
7. Proper speedometer gears for the transmission. These will be determined by the rear axle ratio and tire size. Your transmission builder may have already taken this into account for you but if not there are calculators on-line that will tell you which gears you need.
8. Throttle Valve (TV) cable and carb mount bracket. There are several vendors available, once source is TCI auto. https://www.tciauto.com/transmission-accessories/tv-cables-and-accessories.html
9. PRND321 shifter indicator to replace your current PRND21. These are available from our Avanti parts vendors. You may also need to modify, adjust, or replace the shifting control rods from the gear selector. I was able to re-use my existing rods although I cannot select all the way into 1 on the gear shifter. All of the other positions work fine so I left it as-is.
I was able to use the rear mount and cross-member that were in place for the TH400 transmission. The TH2004R lined up perfectly. You will need to get different bolts to attach the transmission to the mount though as the threads in the TH2004R are metric.
My old driveshaft, with the TH200R4 yoke installed, turned out to be too SHORT so I had to get a new one fabricated. Others have said that they had to get their driveshafts shortened so you may just have to wait and see what you're dealing with once the transmission is installed.
Some other things that come to mind - if you're planning on doing this without the car on a lift, you will have to get the bottom of the car about 20" off the ground in order to get the transmission out. I had to place blocks under my jack stands to get the additional clearance. You may discover that the exhaust system is in the way and preventing the transmission from dropping down. I wound up making a cut through one of my pipes so I could move it out of the way, and just welded it back together when I was done.
Although this conversion is a bit involved, the results are well worth the effort. It really changes the character of the car, especially at highway speeds.
Good luck, and if I can answer any other questions please ask.