You have an Awesome audiophile gear

hope you can share your findings on this topic will be enrich with your opinions.
I 'm not against bass, however many gaming headsets are over saturated with low end because human hearing find it pleasing and can hide bad sound performance. Bass is like salt, gives flavor to a dish but can mask deficiencies or ruin it if is use on excess.
Great to know you understand this audiophiles terms, I tried to avoid them so everybody can understand what we are speaking of.
So yeah in essence, for competitive gaming go for a narrow sound-stage headphone, with very high resolution imaging on middles from 500Hz up to 10KHz on this frequency range: enemy footsteps, friendly call-outs, reload, ambient cues (enemies walking stealth) are mixed in games, stereo no surround.
In lame terms: just like video for competitive gaming is hideous to look at: dulled blacks to see enemies on the darkness, oversaturated reds or yellows(if you are using a colorblind scheme) for outline cues or pop up enemies, etc, for sound you need dominant middle range and very sharp treble. Dynamics are not that important.
Planars are for fast dynamic range.
Mayflower ARC MK2 has a very good DAC that does a great job to outline or separate stereo sound cues and its amplifier is enough to power must hungry headsets. But you can use other choices like K5 Pro, JDS Atom DAC/AMP stack, Schiit, etc. BTW heads up, Schiit Hell doesn't work with consoles, only PC.
Any HiRes DAC/AMP that allows you to connect your console via DIGITAL Audio Input (SPDIF or USB) is preferable than a analog one (3.5mm or RCA In).
I kept recommending the ARC because is the only one I know that pull all these in a small package + Mic input + Analog Audio In Mix, for a very good price.
I think they are working on a slim version without mic and analog mix to make it more affordable.
You are exactly right the best scenario is having a headphone for different uses, mixes or sound applications. IMHO anyone who start on this hobby should have as a starter kit at least 3 different headphones for each spectrum one that does great bass, other that standout in vocals (middles) and lastly one that does delivers fantastic treble for instruments.
Beyerdynamic DT990 Pro's 250 Ohms is in my opinion one must-have or try for competitive gaming, but that's the thing with headphones, same with mice... you have to try them to find the right for you.