Much cursing later it turns out that only this makes sudo tick again:
Defaults env_reset, env_keep="XAUTHORITY DISPLAY"
or, more to my liking in the case of unrestricted sudo, env_keep=*
This recent advisory
suggests that one updates his sudo installation. With the subsequent
result of being trapped in a mess of obscure, badly documented
env_something options, a suggestion of env_check which
doesn't work and no way of
passing environment variables to the sudo'd process.
Great.
