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A general game engine like Axiom or ZoG will never be as strong as a good
engine dedicated to a single game, or an engine tuned to a much smaller 
homogeneous group of games. You always lose some performance in generalizing.
Fairy-Max is slower than micro-Max in normal Chess, because it has to test
all kind of conditions on the move descriptors (such as 'is this piece a
hopper?', 'can it wrap around the board?', 'is it multi-path?') which
in normal Chess is a total waste of time, as the conditions never occur
there.

So I don't think you have to look in the direction of Axiom for strong
Chess programs. Systems like Axiom are designed for ease of implementing
something completely new at a low but acceptable level very quickly.
Strong programs for Chess variants are easier to derive from existing
strong Chess programs, such as I did with Joker80, which is the Capablanca
Chess version of my normal Chess engine Joker.

Such engines can already play under ZoG, as they use WinBoard protocol,
and a ZoG plug-in adapter for WinBoard does already exist. (I am not sure
if it handles the variants, but this iwould be a problem of the adapter,
which should be fixed there.) The problem is that it is a bit pointless to
play them under ZoG, as you could do nothing that you could not already do
their under WinBoard. On the contrary: under WinBoard such engines can lay
each other, under ZoG they cannot. The new Axiom GUI would be better in
that respect, but I haven't seen it, so I don't know how it would match
up graphically.