The 24-120 was a candidate until I saw my friend's VR version. Is the older model smaller and lighter?
I assume the 24-120 is too big for what you want, in which case the 28-300 is also too big.
Older 24-120 models are smaller but don't have terribly good reputations.
The only current mid-range zoom which is reasonably compact is the 24-85VR.
If you want one of the other lenses you mentioned, there are plenty on ebay. I'd probably try the 28-105 since it covers a useful range and has a decent macro mode, not sure how well it performs on the D810 though (it's probably ok stopped down a little). The 50-135 is a good lens but I'd want to pair it with a wider lens.