This is an interesting thread, and if I had read it months earlier I may have gone with a SE amp like the WA5. But maybe not, it takes up a lot more space and cost a good bit more as well. I do know that my WA22 sounds much better when used in balanced mode, so perhaps the whole single-ended thing is a marketing ploy
My other balanced amp is the Alesis RA150 and it doesn't even use XLRs, it has two 1/4" stereo TRS input jacks (in addition to the RCA inputs for SE use). I am using a banana plug to 4-pin female XLR pigtail for headphone use with it. Soon I will have a balanced DAC to hook to it with XLR to 1/4" cables, and it should be interesting to see if that solves the channel noise issue I am hearing in SE mode on that setup.
I had you in mind when I saw the outputs of this amp. The only real conclusion that can be made is that the improvements you heard would have been because the conductors in your balanced cable is of higher quality than the standard cable. In which case one might as well get the better conductor terminated in TRS plugs to retain compatibility with all headphone amps. I'm sure the amp still sounds stellar no matter which hole you use.