Help me put together a $1000 (give or take) headphone rig -- new or used

I've put my big rig to rest for awhile due to life, kids, etc., but I still have a desire to listen to high-quality audio -- Alexa just ain't cutting it.  So I've decided to put together a decent headphone setup until I can rebuild and actually listen to my big system.  BTW, why doesn't A'gon have a discussion forum dedicated to the headphone crowd (hence why I'm posting this in the amps/preamps section)?  Argh. 

Anyway, I'm looking to replicate, as much as possible, the qualities I've built into my stereo system in a headphone setup.  The problem is that I know precisely squat about the headphone world.   So, what I'm looking for mainly is that holographic 3D soundstage with neutral, well-balanced, and natural detail and tonality.  I DO NOT want any artificially boosted bass/mids nor rolled-off or overly "polite" highs.  For you audiophiles, I'm looking for more of a mid-hall/spacial/atmospheric/3D perspective rather than a front-row, in-your-face/head immediacy (unless it's absolutely recorded that way).  Like many of you I'm fairly obsessed with research and reading reviews, so given what I'm looking for I have of course identified some components that sound like they may deliver in large part what I'm looking for.  But I'm also experienced enough to know that what you read can often deviate from real-world performance, so that's where you headphone guru guys come in.  I'm gonna list what would be my "dream" setup based on what I've read, but I'll also list some other highly-regarded components that might actually be better (or maybe even cheaper) than my theoretical ideal system.  So here goes:

Theoretical ideal system: HiFiMAN Sundara, Metrum Amethyst amp/DAC

Yeah, that's all I got.  The BIG benefit of going this route is that I'm seriously considering upgrading to an R2R NOS DAC in my big rig once I get that back up and running, and the Amethyst, which offers a good amount of the proprietary Metrum technology found in their pricier DACs, would be a nice entry into that realm and seems to excel in many of the areas I'd like to improve in my stereo system.  However, you'll probably notice I have not listed any way to get content to the Amethyst, and that's because I'm pretty lost there.  At this point I really just want a streamer that can handle hi-Rez stuff from Tidal, Qobuz, etc. in a high-quality way.  I'd love to put in an Innuos Zen, Lumin, etc. in there, but that would obviously blow out the budget and I'm willing to put that in the "add later" column when additional funds (and wife approval) are available.  Can I start with something as simple as a Google Chromecast Audio thingy for streaming, or what else?

On the other extreme, here's a system on the lower end of the price spectrum that may also largely fill the bill, or at least come pretty darn close, at a much lower price:

Low-cost alternative: Drop HD58X, IFi Nano or Micro

To complicate things further, here are the other components that sounded interesting to me that could possibly be better and/or cheaper than either of the systems above:

JDS Labs Atom
Ayre Codex
Burson Soloist SD2 w/Modi or other
LTA MZ
Chord Mojo or Hugo
Massdrop Liquid Carbon + SDAC
Schiit Modi
Massdrop Cavelli Tube Hybrid w/Modi or other
Bryston BHA
Woo Audio WA6
Drop HD6XX
Sennheiser HD600
Audioquest Nightowl Carbon
Beyer DT990

i have to say the Burson Soloist SD2 has also captured my interest, so pairing that with a good DAC could also be a very interesting option to me.  I know I threw a lot of stuff at you guys here, but I'm really interested in your suggestions given what I'm looking for, especially if you have personal experience with any of these components.  Thanks for thoughts guys (and girls)!