I totally get the feeling that a separate dedicated amp is the way to go.
I have had 30 + amps here, still have a dozen or so...and right now I am using the HD 650's and ADX 5000 (420 ohms) with a balanced cable to the Soekris 2541 and its internal op amp head amp. There is enough power in the Soekris to make either of these cans play very very loud and into its going to damage your hearing range.
I can compare to many amps easily. Comparing to PassLabs HPA-1, iFi iCAN, Schitt Jotenheim, Schiit Lyr 3, Schiit Asgard 3, and others....
Honestly when you level let the amps the sound is very, very similar.
(amps, do not make mega differences but cans...cans indeed make a BIG difference for sure).
Humans are funning beings...connect to an amp, low gain and have to crank up the volume and smile.
Then flip the gain switch to HIGH and WHAM!! Its like its soooo much better.....and all those adjectives.
But take the time and level set and you will be amazed at how similar they really are...
This is a very subjective hobby...and we all here differently.
No right or wrong here....just enjoy!
Alex
...and yes I do like amps....