You can build the 200-4r to handle it, but they were designed as a small, low-friction, gas-saving thing to put behind wheezer 80s Olds 307s only making 125 hp. They were also used in Grand Nationals and other higher performance vehicles, but with a specific build code (usually containing a "Z" in the three letter code). I'm not an expert on them anymore, but I recall that it's not just a different valve body, but a different case itself. The valve body is re-routed and the labyrinth in the case is different. Someone correct me if that's wrong.
I'm just wondering if a more appropriate trans is in order. The THM200, TH350, and 200-4r all share the same length and output shaft configuration, so they're all a direct swap as long as the trans crossmember gets moved to an appropriate spot to match where the mount is. Also, if you do that... grab the shifter parts too or you'll end up with a shifter lever that either doesn't throw far enough, or throws too far and you only get reverse through 2nd. Unfortunately, the only one that can really be built to take the 383's torque is the TH350 which means giving up OD. Of course, with the added torque, losing a ratio and re-gearing the back isn't necessarily a bad thing. I've built several Caddy 500s that I intentionally used a 2-speed Powerglide because there was so much torque that a TH400 was kind of tire-smokingly useless in first gear.
But any trans is possible. 700r4 is longer, but possible to get a driveshaft from something that is the right length, or getting one that is too long can be easily shortened.