
Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.

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Given your budget I'd say yes. My theater-like headphones are $3000+ alone on their own. But Hifiman XE1000SE might be just what you asking for. I think, although they are not as immersive as, say Focal Stellia or Sony MDR-Z1R, the Hifiman is, first of all, within your budget, and it has a ridiculously wide soundstage, which I'd consider it well-compenstaed for not being as musical as those theater-like headphones. My experience with Sony MDR-Z1R is more theater-like than speaker-like, and vice versa with Stellia. I am very sure those two could be what you looking for if you have a higher budget bound. Pair any of them with an R2R DAC like Fiio K11 R2R and you are set.
I have a bias for closed back for low level details & micro dynamics that get lost in open backs unless you really crank the volume. Also sub bass roll off unless you EQ heavy. For me, the dca stealth + hugo2 has been perfect at conveying the entire mix as clean as possible. Unlike other closed backs(stellia) it presents objects in the mix as small & therefore occupying less space in the mix and hence creating a sense of space / openness. It kinda quells my need for an open back. The stellia on the other hand is more dynamic with bigger objects & more defined boundaries that occlude other tracks in a mix. It's intense & tiring, makes me want something that breathes. That said, i have been itching for an open back purely for technicalities that presents the stage in front of my face like the LCD X did. I wish audeze would drop a LCD 5 that isn't tuned as a hearing aid.
I'm on the same quest. Nothing wrong with the ZMFs or Meze Liric 2, but nothing blew me away either compared to my end-game Bluetooths (Solitaire T) or open-backs (LCD-5, Empyrean). Could be that they require a while to break in. Given my recent experience, I'd jump straight to Dan Clark by process of elimination. Not a fan of Focal Stellia due to strong metallic timbre. Not impressed with Liric 1.
If you have the money why not. I love my focal Stelia. Naturally the sound is amazing but they are also just a very beautiful item. Is the sound much different from a decent pair of Sennheisers. Probably not to my ears but they are much sexier.
Sony MDR-Z1R is most certainly missing from that list, got mine for $1000 used. Without a doubt my favorite pair of cans. They are a good all-rounder, made for very casual listening and mainly work with the genres you mentioned, The bass is very deep and impactful, but there's still bleeding/bloat (muddy sound) in 250Hz-300Hz. Treble on the other hand might be fatiguing without EQ and I needed to get rid of their 3.5KHz peak You might want to take a look into the prices of replacement parts before considering this headphone. Another headphone that is barely talked about is the Final DX 3000 CL, elevated bass that is tighter and not as bloated as in the Z1R, but they are currently hard to find. Other suggestions would be: Meze Liric 1/2 if you want to increase the bass, and also the Meze Strada if you are more into dynamic drivers. From Focal you got the Azurys, Radiance and Stellia (still on your ballpark if you get them used). Radiance's bass is wider and slammier. The Stellia's mid-bass is tighter and direct with more kick. Focals are a good decision considering you like a neutral sound. Not sure about open backs but I know the Philphone is a good one, and the Focal Claer OG
My brother owns the Focals and he broke one his Stellia's drivers while hot swapping into the Radiance and opposite. Haven't yet gotten to try the Stellia with original drivers, Focals are decent but not my favorite. I like the my Z1R's more because their sound stage depth makes the bass feel like a shockwave coming from the driver to the earcups, especially with their wide diameter.
Headphones mostly last for a long time, besides all the mainstream consumer stuff that is usually wearing with time or bad QC. Usually you end up with swapping pads or changing a headband strap. There are headphones like the HD 800/S lasting years, and others that have proven their longevity.
There's r/AVexchange, head-fi, ebay, xianyu (aka goofish purchasing via proxy services like superbuy), yahoo auctions (purchasing via buyee), fujiya avic (japanese store) or buying locally. I had experiences with all of those, but always be cautious for scammers / payments. Usually I pay with PayPal G&S because it saved my brother after getting scammed for a Liric 1.
It seems you are accustomed to listening to gear with a pretty wide soundstage... In that regard, mostly all closed back headphones will sound disappointing at first. Nevertheless, Stellia and E3 are two of the best sounding closed-backs in my book.

Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.

Sony
WH-1000XM4
ANC king, durable, but unreliable mic and touch controls.

Sennheiser
HD 6XX
Legendary mids, durable, but narrow soundstage and weak bass.

Sennheiser
HD 490 PRO
Super comfortable, wide soundstage for gaming, versatile pads.

Sennheiser
HD 599
Super comfortable, easy to drive, wide soundstage, open-back.

Ranked #1
Sennheiser - HD 6XX

Ranked #1
FiiO - FT1 Closed-back Headphones

Ranked #1
Sennheiser - HD 560S

Ranked #1
Sony - MDR-7506

Ranked #1
Sony - WH-1000XM4

Ranked #1
Sennheiser - HD 560S