AK is kind of a hard character to make suggestions for since proficiency with him is mainly "be good at fundamentals and do lots of throws". He doesn't have much in the way of abusable gimmicks, outside of WS Giant Swing setups and wall stuff.
Death already went over the punishment, so my only addition to that is realizing that getting better at punishment is moreso learning other characters weaknesses than learning new moves. AK does have super sweet situational punish options (f+2,1, f+1+4, b+3, DU), but really AK can b+1,2 punish several things and be just fine.
Watching over our matches, I will say that I think your spacing with AK might be a bit too far out, relying a lot on crouch dash mixups, backflip and capital punishment to get in. They work on me because I'm a scrub, but it's not the most optimal way to play.
I'd suggest playing in a bit closer around the tip of d/f+1 where you can pressure with that and your lows (d+3, d+4, d/b+3) and throws while also being able to quickly backdash or sidestep and whiff punish with DU. Your execution is better than mine so this gameplan can work for you. If you just feel more comfortable playing further out, then your primary option should just be waiting for a DU opportunity.
Oh yeah, and definitely practice buffering your Giant Swing from moves and blockstun. When you just dash up in my face and do it I can see you inputting it based on your movement haha. 1,2 / 2,1 / f,f,n,2 / d/f+1 into GS are just a few examples. The game is actually very lenient with this, 100x easier than trying to block punish with an EWGF. GS from crouch on the other hand....