I have owned a number of headphones over the years, and now I have the HD6XX (after selling an old HD600), K371, and HE400i (I think the 2016 version...bought them used.)
Based on that, I would suggest you get the K371 and use EQ. I bought my K371 used and don't understand the comments about iffy build quality--mine are just fine. The fact that the cable enters the left earcup is a bit of a pain due to my desk setup right now (just too lazy to swap things around, I guess!)
As for imaging and soundstage, perhaps the K371 isn't the greatest, but if you want to listen to some bass heavy program material, the relative lack of harmonic distortion in the low end makes live rock recordings sound more realistic to me.
That being said, from the results of the poll when I took it, I am one of the 9-10% of folks who tend to hear things to the sides and rear when listening to well recorded orchestral material on headphones without any visual cues. It's almost as if I am standing in the front row of the balcony with my back to the orchestra, but with them in a mirror image of how they normally are seated (violins are still to my left, double bass/low brass to my right.) The famous/infamous Virtual Barbershop binaural recording sounds as if it's all to my sides and rear. When he "goes over the top" of the binaural head with the clippers, it circles around behind and level with my ears. I sense nothing in front of me--and that's with any over the ear or IEM headphone I have used. As solderdudes notes, soundstaging and imaging vary a huge amount between users.
EDIT: And finally, I believe it's impossible to know that your headphones are "properly EQ'd" from listening to a few particular recordings. I tend to focus on whether some minimally miked orchestral/classical recordings sound tonally correct, based on my live listening experience, and then use that as a baseline. The "tilt" of multi-miked pop/rock recordings varies from ridiculously exaggerated bass to unlistenable hot treble, so I use a parametric EQ plug-in in Foobar to adjust those all the time.