So it turns out I'm an idiot. I assumed that because Nvidia allowed me to install a single driver for both of my GPUs, that they actually worked together. As it turns out, the primary feature of the Quadro card--10bit color output in OpenGL applications like Photoshop and, you know, Windows--doesn't work when the Geforce driver is installed, and the Quadro driver won't install at all when the Geforce card is present in my system.
So, I was forced to sell the GTX 1070, even though it is the best card I have ever owned. I am making due with the Quadro for gaming now, but it is far from ideal, as quite a bit of massaging is needed to the settings in order to get smooth framerates on what is essentially a GTX 950 with more VRAM. Nvidia has Pascall offerings for their professional lineup coming soon, but I will probably hold off for Volta at this point. Honestly, as long as I can still push >100fps in Overwatch, I don't actually care that much.
I am also trying to figure out the source of the electrical whine coming from my power supply. It may be that I have a particularly dirty socket next to my desk. Normally, I wouldn't worry too much, but when my entire build is centered around silence, I kind of have to care. It's actually significantly louder than my Noctua fans, the only other real source of noise from the unit.
My next project, now that I have an unexpected infusion of cash, is finishing the Pfsense router I am building in order to unlock the full speed of my gigabit internet connection. More on that soon...