I’ll agree with @Nuance’s comment and advice. It used to be said that there weren’t many decent tube amp options between $500 and $2K. The Quicksilver Audio and the Feliks Audio amps may have changed that, although I’ve not heard them and I don’t know if they synergize well with the HD 6XX or the Auteur.
A few solid state amps to consider beside the Jot 2 and Rebelamp are the Monoprice Liquid Gold X and maybe the Phonitor One (and perhaps other Phonitor amps). With the Phonitor, do please read up about how to plug in and unplug headphones; the volume pot has to be turned all the way down, I believe, or else there’s a risk of frying your headphones. Beware.
The Monoprice amp varies in price considerably. It’s MSRP is $999, I think, but people have purchased it for much less. Keep an eye out for Black Friday, of course. It also has a DAC in it but you don’t have to use it.
Again, I’m not recommending these two solid state amps specifically for your headphones, but they might be worth looking into.