Welcome to the forum. That was… quite a read.
The Beyer DT 1990 Pro is highly regarded for all the things you’re looking for but I’m afraid it’s out of your budget.
I have no qualms recommending the TYGR 300R depending on the price you can get for them. They are comfortable, easily modifiable, provide a wide soundstage, excellent imaging and separation, and warm frequency response while still maintaining detail. At $179 they are the easiest headphones in the world for me to recommend to others for gaming as well as music and general listening, but it will depend how much you can get them for due to various import fees.
I’d also encourage you to check out @Falenkor’s write up here: (update in progress) Falenkor’s Competitive Headphone Write Up. Now with added Hardware explanations! - Gaming Audio / Competitive - HifiGuides Forums