I don't know how you can ever have that solid a read on him. He's always folding AK/AQ/AJ? He never has any of those or any other two overs when he makes the initial raise (because him folding JT here is actually a good thing for you, for instance)?

Assuming everything you said is absolutely true, then just call the bet and shove over his flop bet no matter what comes, as after a c-bet he'll be committed to calling you.