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That rear end will be fine with the 383. It is Beefier than the pre 70 rear ends and they used the old ones (smaller pinion bearing and yoke) behind the L88 (600 +HP). The only downgrade that I am aware of in the 78 rear compared to the early units are the springs in the posi unit are a little weaker to prevent rear end chatter with radial tires. You are not going to hurt it with a small block. The tires might spin a little more than with the 200 hp. powerplant that came in it That will keep the rear from breaking!
There are some things you can do to beef it up but if you're going to push the car then you're going to need stronger rear suspension parts as well- better joints,1/2 shafts, yokes,and spindles.
The carrier in your 78 isn't bad but the stock clutches are junk.The spring setup is the same 400 ft/lb springs they used over the years and tuning would remove them. You can polish and tune the posi and add a steel brg cap with larger bolts, I'm doing one of those job now. Again even with these mods if you get the tires to hook up with a lot of power, it's a load on the rear parts. The ultimate set up would be a Tom's 12 bolt or go solid diff.
Are you going racing or just driving?
I think he'll be OK with a fresh rear rebuild and some HD yokes. He's only putting about 400 - 420 HP to the rear wheels. Running slicks is when the problems start.