I own the HD-800 and the HE-6 but can't say anything about the other cans on your list.
The HD-800 has the larger soundstage, but is picky about amp pairing and extremely revealing, to the point that it's (imo) downright painful to listen to badly recorded pieces or older recordings. It's not a fault, rather a mostly unwanted effect of its extreme capabilities and you have to be the judge if it suits your purpose. I do find that occasionally it's a bit too hot in the treble, yes. But overall it's a very well constructed (supreme comfort), very high quality headphone.
The HE-6: they require a powerful amp but it's a total myth being perpetuated by some people on this site that *only* a speaker amp will work. I drive mine using a high powered SS amp (2750 mW into 50 Ohm) and they're absolutely fine. I also drive them from a dual mono tube amp (which, admittedly, I thought wouldn't work at all but I've since found out that one of the headphones used as a reference to design it was the AKG K-1000, 'nough said). Wrong. They still sound beautifully. Speaker amps can and will work but, liberally quoting from memory from the manual that comes with the HE-6, HifiMan recommends max 70W into 8 Ohm and mentions that not all speaker amps match well with the 6. Presumably this has to do with the impedance mismatch which sometimes causes a hiss/distortion. When properly amped the HE-6 is very transparent (more so than the HD-800) and while very detailed, it doesn't present defects in such a glaring fashion as the HD-800. It also has this totally subjective and intangible 'euphony' factor which makes music really sing, great bass and a good treble which is very occasionally a bit too pronounced, though not as 'bad' as with the HD-800.
For musical enjoyment (classical only) I prefer the 6 myself, except when I'm listening to large ensembles due to the soundstage of the HD-800. Apples and oranges. If I'd have to purchase a set of cans for critically assessing recording quality and reproduction then I'd go for the 800. If for pure enjoyment then for sure with the HE-6. If you get the 6 and have no other top end gear then it would imo make sense to build your entire chain around it.