I concur with @robson about the Bifrost 2 and 2/64. The now obsolete BF2 transformed all my amps and headphones in a good way. The BF2/64 delivered a 10% to 20% improvement over the BF2. It has better staging, definition, nuances, and clarity. In my wife’s words “It’s very gentle on the ears.”
Before moving to the BF2 and RebelAmp more than a year ago I prioritized headphones over DACs and amps. Not any more. If the signal quality degrades early along nothing can bring it back. Nice equipment can mask problems, but the signal is still eroded and has limited potential.
Be aware that the new Lyr 4 (or Lyr+) can switch between SS and tube modes. So you may get a Jotenhiem + tube option for $599, but I have no experience. In SS mode the Lyr 4 uses built in decay mode MOSFETs (i.e., the same thing sold as a tube plug in LISST). I said nice things about the LISST / Lyr 3 combo in the Lyr 3 thread.
I do agree with @pennstac that a headphone tier upgrade can transform your experience. I’m mostly using the HD 800 S and Clear these days – the HD 600 and HD 6XX sound fuzzy, narrow, and truncated.