I know what you mean there. I never put all that much emphasis on sources (past a certain point) or things like cables. With a lot of equipment the difference between different DAC/amps can be minimal.
I've encountered two models that made me be more careful about that. One is the HD800,and the other is the Andromeda. I have 4 amp/dac setups I use often and the Andromeda sounds too bright, cold and lacking impact on two of them. It's just boring to listen to, even a bit fatiguing. With the other two (which probably have much lower output impedance) it's very nice. Much softer, warmer while retaining all the resolution and with a much stronger and tighter bass that really makes you feel those kick drums.
The SE846 didn't seem very vulnerable to the source to me, so in that sense it is a bit more versatile. Bass and lower mids were always satisfying, but I never managed to get the detail clarity and resolution I missed, regardless of source or filters. But your experience is quite interesting... I never tried any cables other than the stock. Gotta say I'm... hmm, cable-upgrade-skeptical, but if jt can be heard, I'll be converted.