So I personally use a pair of WH-1000XM4s but I autoEQ'd them to be the 2018 Harman Neutral over ear target, and I do not get this.

What you are describing is something I notice specifically with open backs. However the Sennheiser HD800S are phenomenal for gaming.

Closed backs for gaming, open backs for everything else is what I'd say you could roll with if you want to hot swap. However, you could use SteelSeries Engine to use their app SteelSeries Sonar (I think) and you can actually set a custom EQ per game, meaning that you could run a neutral target the rest of the time and then tune the open backs to sound proper during gaming.

This is just my two cents, there is always the fact that you're experiencing is just shitty video game settings (should be using Headphones mode and I like to turn on all of the audio enhancements the game offers).