Well he obviously has to call since he has the current nuts. My play is also fine I think.
I had 11 outs minus his redraws chances which gives me about 35% chance to win.
So my play was -EV knowing the cards, but theres alot of hands he could have that I would be closer to even money or a very big favorite.
He flat called with QQ. He couldve flat called with KK and maybe had the Kc.
Some guys would make that same play with KQ with the Kc.
Overall, i think Genius' idea of checking might not be so bad.