I did a similar swap on my '79 Trans Am that has a Pontiac 400. It had a TH400 and I went to a 200-4R. My main reason was so I could run 3.73 gears and have good gas mileage for highway runs with that gear set up.
The mods I had to do for mine were:
-- Correct length TV cable
-- Had to buy the shifter conversion set to have overdrive labeled on the shifter and so it will lock in place when put in gear. Link:
https://www.classicindustries.com/product/all-years/pontiac/firebird/parts/SC226.html?gclid=Cj0KCQiAweaNBhDEARIsAJ5hwbdXy1gy_cySEbNote1fR6Gdc489FIDjQ6dP9vKB47EIYIlo7POxK2QaAiZZEALw_wcB--You will need something to activate the lockup on the torque converter. There are different options out there, but I went with the B&M controller for easy full control of lockup. You can set it to lockup at the speed of your choice and turn it off and on whenever you want. It's easy to wire up as well. I have my control hidden in center console armrest storage compartment. Link to the B&M:
https://www.summitracing.com/parts/bmm-70244--I had to put a higher stall converter due to the aftermarket camshaft I'm running. I also had the 200-4R rebuilt with performance clutches/bands and billet internals parts from CK Performance due to the horsepower range I'm in. A Google search will bring up their website. You should be ok if you're stock or not too far from it, but someone else can chime in if I'm wrong.
I learned that the 200-4Rs are really funny when it comes to trying to get the shift points where you want them. What valve body & governor combination is in it, and rear gear used will determine it. The most sought after 200-4Rs come out of Grand Nationals, Monte Carlos and 442s of the early to mid 80s. There's not really any reproduction parts out there for the 200-4R valve bodys and governors. A Google search on the shift points and shift point modifications of the 200-4R will bring up various ways others have adjusted theirs to the range they found suitable for their set up in the event its not where you want it after install. I was lucky that mine was right where I wanted it.
You shouldn't have to move the crossmember but some have to.