Perhaps with some modications, your built-in wall unit might accommodate a pair of the in-cabinet M60s:

There are photos of some in-cabinet installations on this site and they can be very sleek-looking.
I agree with Catbrat and would not mount the in-wall/on-wall models into a wall unit.

As Ken C. pointed out, it isn't the end of the world if you stick the M22s into your wall unit; it's just that the M22s are marvelously good, natural-sounding speakers and it seems a shame to taint their potentially great sound quality by putting them into a wall unit. Even installed in that fashion, I expect you'd still find there's a large improvement over your old Axioms. Those were quite good in their time (the magazine I edited reviewed them when they were introduced) but the use of the aluminum drivers and titanium tweeters in the M22s has resulted in marked improvements in fidelity and freedom from coloration.

Alan Lofft,
Axiom Resident Expert (Retired)