4 betting JJ isn't bad IMO, it's not really a bluff because we do beat AK and we probably are something like 36% against his all in range. Although we are in position, so calling seems like a good option. I'd probably call here more than I shove, but I'll shove here versus some players.

Oh and about rather shoving AK than JJ. AK is 39% against a range of AK, QQ+. JJ is 36% against the same range, really not much of a difference.