So I've come up with a solution: spirit and intellect armor. Whenever I'm doing anything other than fighting, I'm wearing bright yellow spirit and intellect armor that I got off the AH. I spent about a hundred gold on this dastardly set. It looks awful, it smells awful, and it's a great repellent for annoying unsolicited LFG tells.
I got the idea from looking at people's gear who are apping to my guild. Some of it was just plain nuts – spirit gear on Warriors, "of stamina" gear on Priests, things like that. Of course, they might have just been logged out in that gear the same way I'm logged out in mine right now. But when you're apping to a guild and one of the requirements is to log out in PvE gear for the next week, well, too bad so sad for them.