Ha, no. It was on 60hz, and I tried switching it to 50 just to see if it makes a difference wrt to 3rd monitor. But normally it's 60hz. Switching also revealed the resolution options - they disappear when it's set to 60 for some reason.
Yeah, I was thinking that might be a next step, upgrading to Mojave. I don't have a lot of room for experimentation being that this machine is the backbone of my business, but I do have bootable clones of the system drive as something of a safety net. OS updates just always scare me when I'm in the thick of a heavy session schedule (as is currently the case.)
I got it working! I just unplugged everything and randomly started trying each monitor in different ports until I got all three going, but eventually I got there! I have no idea quite why or how, but I'm going to wait a bit before I mess with it more to make sure it's stable. But at least it appears to be possible.