My only experience with tube amp is with Xduoo TA-26s, OTL tube amp which I managed to get quite cheap. I am running it with HD6XX currently (I have also tried it with other hight impedence dynamic headphones like AKG K240 Monitor or DT990 250Ohm). Frankly either I am completely deaf or there hardly is any difference compared to Topping L70 (at least to my ears). I mean the base rolled off very slightly but overall this is NOT what I was expecting from tube amp, especially OTL one. It is extremely clean, in volume matched blind test I would have hard time picking it out compared to solid state. Maybe just stock tubes are very clean. I tried some cheap replacement tubes but they were just buzzing more but in terms of tonality I could not really tell much of a difference.
At this point I still do not really know what "tube sound" is but my experience is far from what people usually describe. But it glows pretty and catches the eye of guests ;)
That is a good suggestion. I am only afraid I will realize that to achieve this "tube nirvana" I will need to put some serious money on it ;). But hey, we are in this hobby for the journey and the fun of it all ;)