After looking over my images from the Nikon D810 and D750, I've decided to purchase a D750. Both cameras produce very nice images, and I didn't see enough difference to justify the extra cost of the D810. I suspect that my technique wasn't (and often won't be) good enough to fully capture all the resolution of the D810. I don't make prints large enough to put all those pixels to good use. At least, not so far. And using that extra cash for better glass makes sense to me.
Speaking of which: the Sigma 24-105mm f/4 DG OS HSM lens is backordered, with no estimate of when it will become available (a couple of shots with the Sigma I rented are in this post). Instead, I ordered the Tamron 24-70mm f/2.8 Di VC USD, based only on its positive reviews. I didn't see a comparable Nikon lens in that zoom range that has vibration reduction.
For a longer lens, I chose the AF-S Nikkor 70-200mm f/4G ED VR. I liked the results from the borrowed 70-200mm f/2.8 (thanks again, John) but the f/4 is 1.5 pounds lighter, and I don't do a lot of low-light work. It also focuses closer and takes a smaller filter. Oh, and it costs $1,000 less.
So my Pentax era draws to a close. My Pentax kit (Pentax K-5, Pentax 16-50MM F/2.8 SMC DA* ED AL IF SDM, and Sigma 70-300mm F/4-5.6 APO DG Macro) is on its way to the folks at KEH who I trust will defray the cost of my new gear by buying my old (if you have gear you don't want, it's worth looking at their site...you can get a quote and sell gear very easily).
My apologies for not including more images, therefore making you take my word about the comparisons. Useful comparisons are very hard to do, especially when you don't have both cameras at the same time. In any case, the web is bursting with D750/D810 comparisons: images, handling, focusing, controls, and overall sexiness for all I know. Go ahead: spend 59 hours reading and watching them if you like. In my case, I wanted to have my new camera in hand so I can get some time with it before my next trip.
Thanks again to everyone who shared their thoughts and experience!