Yeah, funny how so many assume they know the character and capabilities of Heresys simply from what they read on the web, or their recollection of a 5 minute audition of H1s, twenty years ago. The Heresy IIIs respond very well to system changes, more so than many speakers costing twice as much.
Glad to hear the Luxman yielded such a large improvement. In the future, consider a tube integrated, something like a 20 watt plus Cayin, Line Magnetic, Raven Audio, or Prima Luna. My Heresys perform better in the bass region with my Cayin tube amp than they do with any SS amp. The opposite is true with my other brands. Klipsch speakers crave those valves!