Are you stretching "this specific strategy for parallelizing P that I came up with won't work" to "there's no way to parallelize P"?

It’s more like : you win a Turing award by finding a strategy to parallelize this problem as you’ll be able to use that approach to parallelize all problems in P, proving NC = P.

This applies both ways. You'll win a Turing award if you prove NC ≠ P, which is kind of what you said — at least, that the best way I see of reading your first and a few following messages.