Seems good. You usually create fold equity this way, ie he probably calls with worse hands and pocket pairs that will now (hopefully) check/fold if whiffed on the flop, whereas before you would fold to his cbet 2/3 of the time. You just have to be careful post flop if it looks like you're beat since the pot starts off big.

But definitely fold to the push, unless hes a maniac. I wouldn't reraise if his pfr % is say 2 or will typically call down (or raise) unimproved hands.