This sounds insane, But Id rather be all in then just calling this. If its a race, you have odds. And are not stuck with just a 35% of connecting on the flop and playing the hand OOP.

Id push or fold. Works at my tiny stakes, probably bad advice at your level.

Edit: I just re-read the post and realized he put in a 3rd raise here. I would lay this down, he has to assume you have a monster, doing this with anything less the AA or KK would be crazy.