I wouldn't use HD800's for studio use simply because of the treble. But I also wouldn't use the K701's either.. I know you rate these as great studio cans and I can't argue with that as you are a lot more experienced than me. But its the upper mids/lower treble that may be flat on paper, but the sound is very harsh to me. I would keep wanting to tame the sound if I was mixing with them. My preferred hp for the little bit of mixing I do these days is the HD600's. They are ime one of the most balanced hps's out there. And they were designed for studio use.
Sounds like the K812's may be a good choice for studio, sounds like they are nicely balanced with a little bass hump which shouldn't be too bad.
I would personally use more headphones at once, or just EQ specific one to reach neutral FR (of your already very neutral studio monitors).