SickMetaGame

If its early in the tournament then I shove, if its late then I think risking your life with 44 bigs is too optimistic not that it is necessarily incorrect but I would prefer to flat that 3bet and look what flop brings. Both of the players have playable stacks for post-flop, would lead out all of the boards without overs (sometimes even with an overbet as shove) and give up if there is overs.
Yes you are giving him more equity with this line but I would like to believe that you are going to be behind with ace on flop most of the times after his 3bet and best you lose 9 bigs than 44, sometimes this line helps you dodge KK+ or a flip against AK on board where overs do not hit on flop as op will lay down to our lead and we do not leave him the chance to cooler us on coming streets as we would have no option to avoid when we stack it off pre and wait for dealer to put the cards on board. Yes we will lose some of our equity against that same hand in those scenarios where future streets don't complete op's hand but same time winning 9 bigs is still a good 20% increase to our stack.

Riverbanged is also correct that by flatting we do allow our op a lot of wiggle room to apply pressure on scary boards but at least we are not setting our tournament life at stake. Even if we check/fold to his flop aggression then we still hold a 35 bigs stack.

Check/Call flop. Re-Ev turn. Unless op shoves to your check I would lay it down in a heartbeat if he is TAG.

As played by leading you are setting yourself up for trouble, building the pot big on a wet board with mediocre hand. You are rarely ahead when calling that jam on flop, you are a running dog for FD with overs, insanely behind against sets.

If you say your op is TAG then only reason for leading out the flop I could think of is to fold to his aggression, I do not see him turning his hand into a complete bluff. Easily 33, 44, 88+, JTs+ and you are sweating your balls off with two more streets to come.

I am not sure why would you put OP at described range since inception, to me with his stack size he would be shoving those type of hands pre-flop every time. Also since you are holding one of the aces then him having AK, AQ or AJ becomes even less likely.

3c8s4s

Ac8h (20.99%)
88+, JsTs, QsTs, KsTs, QsJs, KsJs, KsQs, 33, 44 (79.01%)

I did not include any ace combinations because I really think OP would be shoving that pre.

/Muck A8o pre against TAG, especially when you are in your head "sure" that he has something of AQ, AJ or AK in his range, why make your life hard? A8o flops bad most of the times.