I would need more time to analyze what is going on. As I noted though, my current hypothesis is exaggeration of certain frequencies above 5 kHz combined with the larger caps and maybe even driver design. If it is the latter aspects then measuring their effect is beyond our reach right now.
The HD800S has a few things going on that the HD650 does not.
First of all, the drivers are angled a bit so the sound comes more from the front and hits the ears differently than with the HD650 which comes from pure left-right. Some experimentation would be needed to see how this affect the testrig "ears" and measurements/frequency response.
Secondly, the HD800S has largely reflective inner cups. The effect of this is clearly audible and in my opinion contributes to its "spacious" sound.
To test this use completely dry percussive sounds or even clicks / impulses and compare the sound of them on the HD800S with a headphone that has ample padding in the cups. The difference between the HD800 (I did not have the S version) and the Beyer DT1990 I had was quite large in this respect, with the HD800 colouring the impulse of the sound whereas the DT1990 was dry like an anechoic chamber. (to measure this and display it in a waterfall or decay plot you'd need to have at least the reflectivity of skin on the ear and head part of the testrig)
edit:
Btw, I liked the artificial/added spaciousness at first but it wore off after a while.
I found that while it gave some music a nicer presentation, with some other music it got in the way of transparency and "realness", especially with classical music. I could clearly recognise this aspect as the "HD800 added sound" after a while.
For instance the HD800, also after EQ based on a host of measurements on other websites, did not do justice to my favorite organ music which is absolutely wonderful on some dry headphones like the DT1990 and in two near anechoic chambers I heard it on different speakers.
With the HD800 there was no proper sense of 'being there'.