I think you should be able to get away from it - though I never seem to. Like you said, after you call, he's probably putting you on exactly what you have (a big ace). Most people wouldn't try to push you off your hand here with air/hearts once the K falls (AK instacalls).

As for his play, I like the turn push a lot. I think big aces call here more than they would they call a third barrel on the river if the betting goes CR to 210, 300, 500, especially if a third heart comes. If you happen to have hearts, it is a good bet as well.

The check raise seems a little big to me, but in this situation it's sets up the turn perfectly. I don't think I could consistently make my check raises that big though - a lot of the time I want to test a preflop raiser's cb and most people fold equally to a large check raise and small/medium sized on this board if they don't have an ace/hearts, i.e. losing less on bluffs is more important than maximizing value on good hands.