In the end, for networking, I ended up using the Raspberry Pi, and installing software onto it manually (on top of a stock, Raspbian installation). (I ended up using an emulator instead, copying stuff to an SD card, which got installed via a SCSI2SD board.) That all being said, had I had this earlier, I might've used it, at least to get the Quadra up and running. I considered using a VM for file hosting, but didn't like the idea of having to either add a beefy-enough system to power it, nor the idea of using up a few GB on my main system. I also tried an Orange Pi Zero, but had trouble getting the video going.

The documentation on RPi booting seemed a bit odd: some bits were easy to find docs on, but not the whole, or at least enough, as far as I could tell. I gave setting up a bootable SD card a few tries, including doing some repartitioning, but never quite got it going. I figured giving it a shot might be worth it, given that I had heard the Orange Pis had some amount of RPi compatibility. I had the Raspberry Pi already laying around, doing nothing.

Mac quadra 605 emulator