AA facing flop raise on drawy flop, poker stove analysis.

[JROK777]

NL50 100bb stacks

Hero raises pf to $2. Villian calls $2 on the button. The rest of the table folds. The flop comes Qh7h2s. Hero bets $4 into a 4.75 pot. Villian raises to $12-14 or shoves. The standard 2+2 line is to call shove or 3 bet all in. If villian won't raise the flop w/ a hand as good as AQo, we are really behind. I plugged a range in that villian would be happy to get all in on this flop below. I think we are crushed. If we add a slow played KK and QQ to villians range, we are about 50/50. Against a good opponent, in a 2 bet pot pf, we are crushed if all the $ goes in. You guys see anything wrong with this analysis?

Hand 0: { AA } 35.723%

Hand 1: 64.277%
{ 77, 33, AhKh, AhQh, AhJh, AhTh, KhQh, QhJh, QhTh, 9h8h, 9h7h, 8h7h, 7h6h, 7h5h, 6h5h }