Edited my previous post from last night to be a little less rambly(I hope), now that I'm not sleep deprived.
Hoping that someone can confirm that I'm not crazy.
I have no experience with the amp’s and dac’s you have tried. But when I considered a good amp to my LCD3 and HE 500 I come up with (research not listening) Auralic Taurus, HeadAmp GS-X mk2 and Audio GD Master 9. I and up buying the Master 9 and I love it. IMO it smooth, full, dynamic and has a really nice extended treble etc, etc. I’m not saying you should take my word for it and ditch the ones you have at home now, just telling you the outcome of my research.
Having just listened to a few different combos with LCDs and with diff headphones at the NY meet, I had to get to a $10,000 rig to beat my Mojo & PWD II. I think the Mojo for the 3s is generally excepted as one of the best amps along with a 'good' DAC. Usually ones reads that the Gun fits the DAC component.
Different strokes for diff folks, keep what you like, that which you think sounds best.......best advice anyone can give you i think.