Ayre Codex - to keep or not to keep

I'm using a balanced headphone and the RCA out to my single-ended amp in DAC mode.  Here is my concern, when I do A/B comparison using headphones in balanced and unbalance modes, there is a night and day difference in the sound quality. In balanced mode, the music is much more resolving at all volumes (especially higher volumes), with better imaging and sound staging across the highs and lows. Initially, I thought the major difference was just the increase in volume but now, I don't believe that's the case. In general, Ayre's equipment really seem to be designed to be used in balanced systems. Can anybody confirm that in DAC mode, the XLR balanced outs sound noticeably better than the unbalanced RCA outs like with the headphone outs?  The Codex still sounds very good via the RCAs but I'm wondering if there are other DACs in the market, in the same price range, that sounds better in a single-ended system.   With that said, I have few different options, one I can move away from a single-end amp design and get an amp with balanced circuitry (would like to get the AX-5 Twenty for it's out of my budget and AX-7e is not powerful enough for my speakers) or I can look into a getting a different DAC that works better in a single-ended system.  Let me know what you guys think. Thx