Welcome! A Turbo 350 is a lot easier swap than a 400. You can keep your driveshaft and crossmember as the short tailshaft 350 is the same length as a Powerglide. You'll only need to change to a fine-spline transmission yoke. It's virtually a bolt-in. With any 400 you'll have to change the crossmember and the driveshaft will need a bastard u-joint because of the difference in yokes. The 350 uses a cable kickdown instead of the Powerglide mechanical linkage, but all you need there is a kickdown bracket for the cable that any Camaro vendor sells. Depending on your torque converter, you may even be able to use your PG flexplate and starter. You didn't say what shifter you have i.e. column or floor, but that's easily addressed.
Unless that 383 is a killer, a 350 will live behind it. No question, the 400 is stronger. But it also has higher parasitic drag internally and a less favorable 1-2-3 gear drop than a 350. Hope this helps and good luck!