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Synthetic engine oil

Is it OK to use synthetic oil in a 67 427 390 Corvette?

If the engine is unmodified and toleranced as new, and the oil is the correct viscosity and contains all the needed modifiers such as ZDDP, then internally it makes no difference whether the oil is mineral or synthetic.
I think the issues with synthetic arise because it tends not to play well with the material in older style seals and gaskets and could lead to leaks and oil sweating.
If it’s as described, I’d just continue to use a quality mineral oil in the correct viscosity and needed additives. Besides, given the common use of such a car, you’re not likely to put all that many miles on it between changes and those miles aren’t going be hard ones anyway. So not much advantage…IMO, to synthetic.

The other thing, which you briefly touched on, is zddp. Most oils formulated for newer engines lack enough zinc and high pressure agents to support a flat tappet cam. Most newer engines are either overheard cam, or hydraulic roller. Neither of which require the higher zddp agents that our older cars with flat tappet camshafts do.