You have to shove this, otherwise you allow a reg villain to play perfectly. I'd expect any reg just to flat Ax against your sizing, as they'll know that shoving over your bet achieves nothing other than getting snapped off by quads, paying extra rake for a chop and getting folds from the rare amount of time you're bluffing. I just don't see worse than Ax calling either.

Same applies to when you river a boat when an obvious flush draw comes in.