OK, I've run kickstart with every combination of options I can think of, starting with
kickstart -activate -configure -access -on -privs -all -restart -agent
Chicken of the VNC says "Please configure Apple Remote Desktop to allow VNC Viewers to control the screen. Unknown authType 30"
So I set up VNC access with a known password on another computer, and confirmed that it worked. (What happens when you VNC into the computer you're already on? Do you remember that scene in "Being John Malkevitch" in which John Malkevitch himself goes through the tunnel?) I then copied the /Library/Preferences/com.apple.VNCSettings.txt file from this known computer to the target computer, tried Chicken again, and got the exact same message.
So I deleted the aforementioned file on the target machine, figuring that would take me back to some sort of factory default settings. Chicken -> same message.
kickstart -configure -vncpw <contents of VNCSettings.txt file here> -restart -agent
Chicken -> same message.