Probably impossible to determine without a direct test-fit. A couple things I'd look at though. 1st, check the actual transmission part numbers. I'm unfamiliar with the Axiom trans, but if it's also a 4WD TOD, 4-speed trans, then it's likely got the same internals as the VX trans. As an example, my Mitsubishi GTO runs the same ATX trans internals as the AWD DSM's; the difference is the bell-housings. Second, I'd verify that the location of the trans is in the same spot in the Axiom as in the VX, and that the bay layout is fairly similar. Getting overall external measurements should help.

The good news is that if Axiom engines are fairly plug/play, then the Axiom trans should also bolt up fine. It's just the clearancing that might present a problem.