Two new Xfinity techs are here. They took a look at the wording behind the coaxial wall plate; It was ancient and apparently there was an incredible amount of signal noise. They replaced it.
But it's still a mystery as to why rebooting the router fixed the problem about 70% of the time. So we're going to have to wait and see what happens. If it starts crashing again, it may be that the router is being interfered with by electrical noise that's not on the coax, but on the power supply. But it's plugged into a UPS, so that shouldn't be the problem.
It's also possible that one of the four devices connected to the router by Ethernet could be kicking back somehow, but again that's going to take monitoring to figure out.
Right now we're hoping that the problem is solved. They gave us two new CAT 6 cables to connect the modem to the router and the router to my desktop.
And while he was down there, Sebastian discovered several unused USB ports in the back of my computer. Don't know how I missed those before! That makes eight ports total. So now I can hook up several more SSD drives.
Here's hoping this is the end of the matter!