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Right after the XDMCP class diagrams, there's a secton on VNC server support. lightdm has a VNC proxy delegator thing built in!
So fornicate systemd, I just need to add a stanza to lightdm's configuration to listen on port 5901 and call Xvnc. Which I did. And it worked in just a few tries. Success! Tuesday afternoon, maybe 10 hours after I started.
Rebooted a couple of times to verify it's really working, and it is. So now I can move on to the next thing.
10/N
#LightDM