I have 4K to spend on a better headphone system and have no expertise in the headphone zone.
Currently using old Grado SR 225 cans with Schiit Jotunheim 2 amp (single ended connection). Source is Jay's CDT2 transport and I'm using the internal DAC in my Hegel H390.
While the Hegel's onboard DAC is pretty good, it is a bit thin in the mids. I'd prefer something a bit more fleshed out in that frequency range.
I'm not finding many headphone amp/DAC combos. I am not interested in Chord or import brands that cannot be serviced in US.
The Teac UD 507 looks like a possibility. Moon Audio sells it and recommends HiFiMan HE100 V4 Stealth Magnet currently on sale for $949 to pair with the Teac.
Please Note: This budget will also need to accomodate a power cable and an AES/EBU cable to connect to transport.
In terms of sonics, I favor musicality over detail. I'm very sensitive to fatiguing highs. At the same time, I prize tight bass.
I listen to 3 types of music: acoustic Jazz, non-classical acoustic (NewGrass, Singer-Songwriter, Folk, etc) and some Classic Rock.