Subwoofer for Ayre AX-7e?

As someone who loves his AX-7e so much he had Ayre install high-pass crossover caps so he could use it to drive a pair of Quatro CTs, I’d build your system around this component. I used to drive a pair of monitors + subs, but my GMA Callistos could play -3 dB @ 47 Hz (I think), so my subs (plural) would cross-over around 40 Hz. Subs would cross-over much higher to augment the Epos. I’d spend your sub budget on fuller-range speakers. I’m also a big fan of the Ayre / Vandersteen combo. 

As someone who has ownand used a pair of Vandersteen 2WQ's for many years I don't think either they or the new Vandersteen subs would ever work with the speakers you have now that have a minimal bass response in the 50's hz range.That is not the type of speaker they were designed to work with.  I like other posters would recommend you look into a full range speaker first whether it be the venerable Ici or even a used 2CE Sig.  There are also many others so you need to get out and listen for yourself.  

@jazztherapist if you do decide to move on from the Epos and continue building your system around the AX7e, one thing that may help narrow the search is focusing on speakers that are reasonably efficient (at least 87db/watt) and a relatively easy load. E.g. stay clear of 4 ohm speakers, 6 ohm and above with relatively stable impedance curves are better. The AX7e uses small output devices and is not a high current design so it doesn't deal well with dips and swings. That may be one of the reasons the Vandersteen 1ci works well, it is specified at 6.8 ohms +/- 2 ohms which is very stable. My current speaker is relatively efficient and forgiving, and does sound good with it, but I do think it could be better with a more powerful amp - the maker told me it loves current (Dynaudio Esotar drivers are known for being that way). I have things at the other end of the spectrum lined up (e.g. Bryston 4B3) to test that theory.

@jackd ,
The Vandy subs use crossovers at the 80 to 90hz frequency, so will more than likely be able to work with just about any speaker.
The OP could use the 2wq's with his integrated if he sent it to Ayre to have it modified to include the crossover caps. But, it would make more sense to move to a pair of Vandersteen, as well.
B

Just as a reminder, with no offense to the Vandy crowd, there are also many other good speaker options. ;)