I do mixing as a side job.. It all depends on your habits, someone prefer to use headphones with certain frequency ranges emphasized as a sort of psychological brake, knowing his common mistakes (i.e. overemphasizing vocal presence region) and trying to compensate them with a headphone that neutralizes that common mistake (for example a heapdhone with exagerated pinna gain zone). Or... you can be in search for the better translation possible between your speaker-room system and your headphones, when speakers are used as your main tool, and heaphone are just a secondary check. Or you can aim for the flattest possible reproduction in your headphone, given your own concept and perception of neutrality.
In my case I have the last two goals.
LCD-X 2021 is a widely used tool among mixing engineers: I did not try them, but from graphs I’d be a little worried for the pinna gain zone, too recessed for my tastes and perception of neutrality and translation in that zone. My choice is the Monoprice M1570, that is known to be 'inspired' to the Audeze line and has a similar driver. The M1570 comes with two pads: with the pleather one the FR is very similar to the LCD-X, while with the velour one the pinna gain is more forward, more or less on harman target; I find the velour pads more suitable for mixing, while the pleather are too forgiving, and tend to mask any (crucial) error done in the 2K-5K area.
The M1570 also costs half than the LCD-X. If you do a search, a lot of people who tried both the LCD-X and the M1570 prefer the latter.
Today, if I had the money I would buy the Modhouse Tungsten for sure, but it outside your budget (and mine).
I have had the Arya Stealth: No... not for mixing, for me.