54% isn't really a lot, but without reads I think a c/f is probably best. Some players will just autobet flop if checked to so if you have that read a call or c/r might be better. Vs tight/straightforward players you can bet smaller and fold to a raise.
Pot/calling is probably your worst option but I don't think its egregiously bad or anything. There's just no value from exploiting your opponent, only a little bit in hand protection.
This flop isnt good for your range, even if you are 3betting BTN from the blinds with a high frequency you're just not going to have a tonne of strong hands like straights on this board, the top of your range pretty much being AA + clubs then the rest of your range is like some overpairs & a bunch of middling to high run downs that completely whiff. With that being said it doesn't make sense for you to pot this board (let alone cbet it at all) and commit yourself with a hand that's not going to be happy calling off the shove.
Why did you bet so big on the flop? What hands are you trying to get value from? He is folding all of his missed high cards or medium run downs, so you will only get action from hands that you have poor equity against.
If you are planning to bet/call like this, then you are probably better check/shoving. At least that way you might entice a few bluffs into his range.
I assume his open range on BTN is 54% as raising range can include 3b's and facing limps.
54% open means his liekly hand selects pretty strong. So the 1 paired hands will have other connection.
It is a tricky spot but stacking off 40$ to defend your 5.75 investment pre seems easily exploitable.
I don't like these aces by the way, I would just flat or 3b a smaller amount. I don't tihnk that potting is pushing value, you don't own much of the deck and are OOP with an SPR which is in his favour. I know you said you been 3bingb alot pre but I don't balance these aces into a pot size. The aces are strong if he is easily induced post flop and your 55% vs his shove range is plausible. It is not reliable however to assume enemies are this weak.