In the Corvette world, there are a few true experts. One of which is Gary Ramadei. He rebuilds rear ends and offers his expertise to all.
While synthetic oils are better than dino in almost all respects, this may be an exception.
Synthetic gear oil will probably work fine in your C3. Most of these cars are hardly driven and not really beat on.
I am running the GM additive and (probably) Valvoline gear oil in my rebuilt Corvette rear.
Here is an article by Gary for your reference:Diff Rebuild
Near the bottom is his fluid recommendation.