I’m afraid this post won’t be add much to what’s been posted already, @Works4treats, but I’d like to echo what Polygonhell has written, and at the very least I can offer another data point for you.
I’ve got the Massdrop Cavalli Tube Hybrid, the ZDT Jr., and the SW51+ and I also have the HD 6XX.
The ZDT Jr. is the best of these three amps for a deeper, wider, more three-dimensional soundstage and for tubey gooey pleasure. It’s a great amp. One limitation of it is that its bass isn’t the tightest but I’d assume this isn’t a priority for you given that you like the HD 6XX. The ZDT Jr. is quite warm, depending on the tubes you use, and the treble isn’t the most well extended, which partly explains that warmth.
The MCTH has a significant bass emphasis but, again, it’s not the tightest, and it can be a bit boomy. The midrange is decent but not very rich, and there’s a bit of treble emphasis. The MCTH’s pairing with the HD 6XX is decent enough; it’s quite clean and has strong macrodynamics - drums sound nice and quick and strong and clear - but this is a far cry from the tubeyness or holography you’re after. I’d skip it for the HD 6XX.
The SW51+ is a neutral amp. I’ve not thought of it as dry but then I have the Bifrost 2 as my DAC; I’ll go listen for this dryness when I get from vacation. It may be something I’ve overlooked. Again, this amp’s not ideal when it comes to tubeyness. But it does have plenty of magic with the mids. Of the three amps, it pairs the best with the HD 6XX according to my preferences (which, to be clear, are in favor of the HD 600 over the HD 6XX, which I find too warm, especially with the Bifrost 2 and ZDT Jr.). The soundstage of the SW51+ has acceptable depth. It’s not three-dimensional or very spacious, but with the HD 6XX, it’s quite wide. Imaging, layering, and separation, though, are excellent, for the price (and compared to the other two amps).
I’m afraid I’ve not heard the Valhalla 2 and my experience of the Lyr 3, from brief auditions, is entirely insufficient to warrant offering any comments.
You might also consider the Vali 2+. I’m not sure how well it pairs with the HD 6XX but I know a number of people whose ears I trust who have commented on its quality with the high-impedance Sennheiser amps. It has the advantage of being well under your budget, and it may well punch above its weight, especially if you can’t get ahold of the others we’ve been discussing here.
Your best place for info about the SW51+ is over on SBAF. Sign up! You don’t have to be a well-established member there to order the amp (I’m not sure if you actually have to be a member although the maker of the amp, Zampotech, originally made it for that community). I’m not sure if he’s currently taking orders for a new batch the amps - you should check his recent posts.