Running into the effects loop is an idea, but the D800 doesn't have one, and the GK is again a tad bulky for requirements (however both would get the job done at a stretch - this is me being picky about my sound).
I believe that you can run into the aux-in of the D800. You might need to determine the proper adaptor for that.
A used Eich T-900 has popped up on bassdirect for a good price, I might have a look at that!
Here is the demo of the Eich that I mentioned earlier. Be sure to read the description so you know what's going on (particularly with regard to when it's pre-EQ and when post) and listen with decent headphones or good speakers:
I don't have a lot of experience with the TecAmp Puma, which preceded the Eich -- I played one a couple of times, but not side-by-side with the Eich -- but, to my ear, the Eich is a little crisper, more open, and more aggressive (which folks might or might not like). I don't think it's a totally neutral amp, but neither is it as heavily voiced as some. I think it could work well for what you're looking to do, if you like the basic sound and the EQ.
Be advised that it has a pretty wide-open deep low end -- can get the speakers pumping if you're playing loudly. You might or might not find it helpful to run it with an HPF (which some external DB pres will have built-in). The T-900 model certainly has the juice to strain a single, smaller cab, so utilize good judgment if you go that way (particularly if folks will be sharing your rig).
Check out Aguilar Tonehammer series.
I know you can dial these in fairly clean (used to have a TH500), but would you consider that amp conducive to "sparkly, shimmering," wide-open highs?
Actually, OP, if you play through an amp that has a ruler-flat frequency response and very low distortion, it might not sound all that sparkly and shimmering to you unless the source already has that. The
tiniest bit of distortion and/or even a very gentle rise in the treble (which you can dial-in if the amp is open up-top) can help get that across.
It is possible to have a very present, even "bright" treble sound without extending so high up, but you might find it to be qualitatively different than what you're looking for.