$50R: Bax overpush with AK from the bb...from pokerxfactor

[guaranteedBluff]

The situation is this:

Blinds are 100/200/a25

Middle position (t8000)
JohnnyBax (t12k)

Bax is dealt AKo in the bb. MP raises to t800, all folds to bax, who pushes for (effectively) 40bb, and states, "I don't wanna play this hand out of position so I just shove all of my chips".

Now, I question a few things about this play:

1) Does MP call with a worse hand? I doubt it; such a large reraise really smells like AK, and I only see QQ+/AK calling, maybe throw JJ in there, but definitely not AQ.

2) Is there a better play than this? A smaller reraise to say t2400-3000 makes the hand awkward to play given stack sizes, so it seems cold call is the other option. Cold call obviously gets more value from AJ, AQ, KQ when an A or K flops, but maybe gets pushed off the best hand when low cards come and MP fires a continuation bet.

Clearly, it is more difficult to play the hand by just cold calling. However, this fact does not necessarily mean that it is less profitable... any thoughts?