I'm not going to beat a dead horse into the ground so I won't respond after this for the sake of being redundant.
Again, I have in my estimation a medium type grade of Tinnitus. Not sure where you're at with yours but finding headphones that suite your tastes and to alleviate the ringing (getting worse too when listening) is difficult. You say you were going somewhere to audition some headphones but it doesn't look like they have a full line-up so that now makes it doubly difficult because you'll miss out with a lot that's out there.
With my Tinnitus, I've found that the ZMF line is great for build quality, customer service, workmanship, warranty work if needed and most importantly quality sound. And my Tinnitus is bothered less with any ZMF headphone due to the way they're tuned. They're smooth, detailed, colored more to the warm side, great bass and smooth treble. The mids are spot on and I'm talking about everything Zach manufactures himself "by hand" one at a time. You have a budget of $1000. That's pretty good and you can get quite a bit of headphone with that budget.
I owned the ZMF Atticus and it just killed. Probably everything you're looking for but it's a closed back. Then the Aeolus which is basically an Atticus but it's an open back . In my most humble opinion, it's a lot better. Just a killer sound. Beautiful too. This headphone punches WAY above it's price-point and competes with headphones double it's price.
Also, the ZMF Ori/Omni (which I also own) which I believe that one is up for sale right now in the classifieds for about $500. Another awesome headphone that's great for my Tinnitus and just kills it.
Man, I could go on forever about ZMF but it's your cash, your ears, your taste, yadda, yadda, yadda. It's too bad you can't check them out because I truly believe from what you "describe" you'd really like what this brand sounds like end to end.
I also own the Klipsch Heritage HP3 but that's another long story. A GREAT headphone that's underappreciate that contains many of the attributes your looking for. If you want any info about these, just PM me. The Audeze LCD2 classic could be another choice IMO it doesn't come close to anything ZMF.
It sounds like I'm a ZMF fanboy and maybe I am. If you REALLY like something, you're a fan and I'm male?
The Aeolus truly is a very solid choice if interested. If you don't like it (which I'd be hard pressed to think you wouldn't) they sell really fast when they do come up in the classifieds.
Anyway, it doesn't look like you've jumped on anything yet so good luck to you in the hunt. Please be sure to update us on whatever you choose to suite "YOUR' needs and preferences.
Regards