His 3bet% is big enough to go for value but I've lost that much calling AK off PF to be up against AA KK or flipping at best like you say. If he's got AK here your shoving it into split. If he raises you like he did you get the feeling he's trying to commit you to the pot with AA, KK or QQ.
I actually like calling his raise and playing it 4 way, AKs plays fairly well in multi way pots IMO, if you hit your draw your gonna get odds
to play for it most of the time. If an A or K come then there's less chance of you getting stacked with TPTK with 2 extra players in.
As played I don't think you have an option not to get it in as your getting the odds to flip and are committed at this point. His 3bet% warrants it as though its a low sample he may be capable of doing this with TT-QQ, AK you chop, AA and KK well at least your suited
DO you have his VP and PFR by the way?