Well, SSH worked, but not in the way I wanted. I could use the command line, but I couldn’t run an Idle session, for example.
However, I found XRDP, which does exactly what I was looking for.
I installed it on the RPi, and then connected from my PC with Windows Remote Desktop.
Perfect. I can run Python programs on the Pi, using PC screen and keyboard, with the Pi monitor disconnected.
My little robot is most pleased that it doesn’t have to lug the screen around!