Solution Found

 
Sony A7II, FE 28-70 f3.5-5.6 OSS

Well, I think I've found my solution to the question of what body to use to cover all 4 of my use cases.

The answer is a D750.  It's just about 250g lighter than the D800, has a nicer finder (same one as the D810 in fact), better handgrip, a flip-out LCD and Wifi. And it's faster at 6.5fps (vs 4 or 5 in crop mode for the D800) and has dual SD cards, instead of CF+SD (I don't own any CF larger than 8GB and don't intend to buy any as they're obsolete cards). Oh, and Auto-ISO respects Non-CPU lens Focal Length on later firmware versions.

The downsides are the loss of some physical controls & build, and the viewfinder dimming outside of the crop area feature.

The mixed blessing is the sensor. I lose the crop-ability of the 36MP sensor, and the useful DX mode, but the D750 has 1.2 crop (unlike the D6x0's) at 16.7MP and is better at high ISO's. And I've long known 24MP is more than enough for my actual needs.

So I traded the D800 for a D750. We'll see how it goes, but I expect it will work out pretty well. It feels better in the hand than the already excellent D800, and a few of the things I was missing with the D800 (flip-out LCD and Wifi most notably).