I'd need to know how big the stacks were to start, but I'd say 1 of 2 options is better, depending on stack size and goals.
#1) flat and jam on a favorable flop (stop n go)....so if you have an over pair, or if the flop contains just a J or a Q but not both, and no A or K.
#2)3bet jam preflop to get max fold
equity and eliminate your positional disadvantage. If you've already figured out that you're not going to fold to his 4bet shove, then you may as well just shove yourself since TT is a vulnerable hand.
as it turns out, he wasn't going to fold AK to your min raise or your jam, but for his range, he probably would have folded quite a bit of his range if you jammed pre, or if you jammed on a flop that missed him.