I would strongly disagree with the HD800 being unable to play complex passages in the music source loud and clear distinguishing the different layers of any added to the music itself, the HD800 is one of the best classical players which for one some classical tracks possess more complex multi-instrument passages than even the most distorted and heavily mixed electronic music, the HD800 can play and render the separation very clearly quite well enough that I'd personally put it easily above the ranks of the typical Lambda's.
This is of course being powered by any high end SS that not only pairs with the HD800 by synergy but also delivering the capable voltage swing for the wonky impedence the HD800 possess. I would also say that a lot of TOTL amps even such as the Stratus takes too much away and in a way veils the HD800 sound signature. The GSX MK2, ECP L2 and few of the Luxman TOTL amp's are a few very well regarded amps to pair with the HD800 that tones the treble down a bit.
Also the reason why you and a lot of inexperienced Lambda users perceive the treble to be clear and earspeaker capable of separating complex passages more clearly than anything else is because there is a treble etch present on a majority of Lambda earspeakers. HD800 performs this role more naturally despite the peaky 5-6k treble.
Refer to the old Stax threads.