What is the most fun way to set self-important Wikipedia admins on a wild goose chase for ghost socks?

I'd say mess with their pet articles logged in with a username that sounds suspiciously similar to that of a user they've hunted.

Administrators do not check for sockpuppets, Checkusers do. Checkusers are highly trusted users who have a tool that can look at a user's IP address. It is not really possible to trick them, because they are rather experienced in dealing with such things and they do not block users by accident often.

I'd say you should steal a Cadillac, go to a Nevada brothel, get really, really, drunk, pass out on the floor with about a dozen prostitutes, and then wake up naked in the desert lying in a pool of your own filth with $200,000 in stolen cash and a rocket launcher. (If you're female you could go to one of those Malaysian sex clubs and do essentially the same thing, except for the rocket launcher - but I'm not taking anything for granted here.)

It won't change the behavior of any Wikipedia admins, but you have to figure they'll accuse as many innocent people as possible of multiple-account abuse anyway, and you did ask what would be the "most fun."