"I own the HE-5LE's and I also owned an Audio-gd Phoenix, the Pheonix did not drive the 5LE's well. I purchased a Schiit Asgard not really expecting a magic bullet, but the truth is that the Asgard made the Phoenix sound broken. The Asgard drives the 5LE really well, dynamic, full bodied, with good transparency and a nice sweet (but not syrupy) high end.
The HE-5LE and the HE-6 have different drive requirements. The HE-6 is a little harder to drive than the 5LE. So, even if an amp drives the 5LE sufficiently, it doesn't automatically mean it will be a good match with the 6.