Considering Wadia 860

What are you looking to spend? There are a lot of other digital sources out there that DO NOT use digital volume control and offer a greater ease to the presentation of the music; i.e. a lot more musicality.

Answering your question about SE vs Balanced, if your amp has single ended inputs only, the wadia would be as good on SE as any other Cd player; in theory that is.

I cannot judge the 860 against the 861 but as you mention the word "sound character" it seems to be obvious that you love the Wadia DigiMaster's algorythm approach - as I do. So if you have the 860 I would not upgrade to the 861 but go further to the 270/27ix. That's the real treat!
I fed my 27 into Mac tube gear via single ended and balanced. If your cable length isn't an issue, single ended is ok. Since the Wadias are "true" balanced units it is always better to stay balanced throughout your entire system - if possible.
Good luck!