I don't think if partner bid 3♣ over my x that I would pull. I have a ruffing value and three pieces. If partner wasn't sure 3♣ was the best spot he could have bid 2N. I realize we aren't necessarily in the best spot but I'll take my lumps there.
Yes I would gladly x 2♠ with 4036 for the same reason.
Shouldn't 2♠ really show a prebalance with 4-5 or 4-6 though? Assuming we our overcalling strategy isn't pre-Cambrian what else can 2♠ show??