As the number of clauses increases, so should the number of variables (randomly chosen).

Why should it? You didn't say anything about that.

Even for overconstrained values of alpha, the problem is still in NP, i.e. exponential in the worst case. Being able to make an accurate prediction for overconstrained values is certainly possible, but would we call that heuristic an "intuition"?

I don't think there's a difference between heuristics and intuitions, or rather, I think many intuitions may just be how heuristics feel on the inside.