There is, happily, an alternative dock that runs on a Thunderbolt connection which is now available on certain PCs (including this laptop). We were able to order one through Procurement and it arrived today.
I now understand why they don't just hand this dock out as standard issue.
The first thing that you have to understand is that the instructions for this dock are pretty much entirely pictorial in nature, sort of like the sort of thing you'd find in a cheap product from the Far East. (Oh, right. Lenovo. Never mind.) And they are not *nearly* as good as, say, Ikea's pictograms.
The Thunderbolt 3 cable for a PC (and perhaps everywhere) is in exactly the same form factor as a USB-C cable and fits into a USB-C port on the computer. This is the *wrong* port to plug this dock into (although it was the *right* port for the USB-C dock). The problem is that the Thunderbolt symbol on the computer is *in between* the USB-C port and the really odd looking Thunderbolt port that takes the same cable. I found out about that problem by searching the Internet for other people who were having dock problems. Once I got the cable into the right port, I was able to get the monitors to light up. This was progress.
The keyboard and mouse, however, were inert. Was this a problem with the KVM switch? Maybe. But I decided not to try unplugging them and replugging them in directly for the moment as I continued to fiddle with the keyboard and mushpad on the laptop. I find in the fine print somewhere an instruction that says to plug the USB cable for the keyboard and mouse into a *particular* unlabeled USB port on the dock. I guess I can try that. But still no luck.
Using the keyboard and mushpad on the laptop, I manage to navigate to the Windows display controls and reset the preferred monitor resolution to 1920 x 1200. The screens fill up the way that they should. Victory!
Except that I still don't have a working keyboard and mouse.
Well, let's shut the whole thing down and restart. Turn off the laptop, turn off the dock, power up the dock -- oh, look, that powered up the laptop -- type in the encryption password, boot into Windows 10, and let's see what happens next.
And look! There's a message on the monitor that says something to the effect of "Installing Thunderbolt devices". That would be good. And then a dialog pops up telling me that Thunderbolt devices are trying to access my computer. One of the choices is "Yes, let them do it. Every time I log in."
And then the keyboard and mouse started working.
Then the VPN that I connect to with a VPN appliance decided that I needed to authenticate again, because I was now using a different dock. Ok, let's do that.
And now everything works.
I believe the phrase that best describes this process is "Goat Rodeo".
Let us *please* never give this dock to someone who is not technically inclined.