Keep in mind the slightly wider/deeper soundstage on HD800 comes with a slight distantness to its sound that pulls against its analytical capabilities.
It would be unfair to say that HD800's sound is big and diffuse, but there's some of that when compared side by side with different yet similarly capable headphones.
K812's sound is more raw, more upfront, more of 'placing your ear at the recording's microphones' so it's probably the most analytical between the two.
What I'm saying is:
"ridiculous soundstage + crazy good imaging + crazy analytical properties"
You might not be able to maximize them all in one headphone, so at the end of the day you'll have to weight their attributes and character acording to your preferences.
The extremely good and very expensive Utopia for instance will give you tons of performance, but no ridiculous soundstage.
Anyway, these are all very good headphones and considering you enjoy your similarly tuned K712, best chances are you'll be happy with any of them if you ever decide to upgrade.
All of them HD800/HD800S/K812/T1.1/T1.2/Utopia are a tad better than K712 here and there.