As played I think shoving the river is fine, he rarely has 99/55/TT in this spot and JJ/KQ/88(maybe) are getting a good price to call.

Betting the flop bigger with your value range is a good idea, it's fine to bet smaller with air like AK since he won't notice. So $2.20 and shove turn seems good as well since he's not folding most hands to a slightly bigger sizing. Your line is good since it keeps his range wider but sometimes the board runs out bad and stops him putting money in.