Tbh, I would sometimes (mostly without history on villain) jam it and rep one of the million busted draws out there and make him hero call it with Ax. Than again, I would also do the same with my busted draws in that spot sometimes aswell as Kx 9x hands. It helps your image, puts him in a tough spot with Ax and you start creating some dynamic. If he calls with Ax he's most likely to get frustrated (people tend to get really frustrated once their hero call fails), if he somehow calls and you show a busted draw he will mark you as a fish and next time you will know what he thinks of you and will be able to play your FH for max value shoving there.
Than again, I maybe be overthinking and betting 80-120 seems fine aswell.
Would love to hear some opinions on shoving our hand in this spot as it looks interesting
(atleast to me)