[well named]

Against a range including {KK+,AK,33,99,K9,flush draws} you're about a 45/55 dog, but even with 0 fold equity it's about neutral EV at worst to shove with the dead money in the pot, so I think it's OK to just stick it in. Add a 10% chance he's an idiot who would do this with other top pairs and it must be at least slightly +EV. There will be a lot of variance, but I just get it in here and see what happens.

Edit: nebben, jinx. I swear I didn't see your post first. I think it's marginal but if you're properly rolled and can handle the variance I don't mind flipping a coin here with perhaps a small edge. If nothing else I'll try to make use of the image it affords me.

Also, I'm not sure your EV calc is correct, but i'm just eye-balling this. After BTN raises to 4 your 1.20 is dead so I'm counting it as part of the pot. Basically when you raise the flop you're pricing yourself in to shove I think.