1) Be the Insane.
2) Use a useless weapon which looks cool. I usually use Thunderfury.
3) Find a pretty dress. I went with Scarlet Sin'dorei Robes
4) For my pet I went with the Phoenix off the same Kael'thas.
5) If you can spare the defense loss, put on a hat as well. I used Crown of Destruction most recently, but Corp'rethar Ceremonial Crown also sets your head on fire. Repelling Charge is a great way to fill in missing defense.
6) Pygmy Oil.
7) Joke around, be silly, be insane, don't feel like you have to silently pull as fast as you can.
8) Run with a friend, so at least one person won't vote kick you. :)
In other words, recognize that most of us are so completely overgeared that we can afford to throw out stats for appearance. If you lose some DPS or avoidance or health or regen, so what? I'll take a one minute longer instance in exchange for enjoying myself during it. Less efficient? Only a moron would say that. Unless you derive inhuman amounts of enjoyment from the acquisition of badges, odds are you're going to have a net gain of happiness, and higher average happiness/time if you slow down ever so slightly in order to have more fun in the process.
At this point I don't even have much to gain from randoms. I have all the triumph gear I want unless I lose my mind and go holy. I don't need the gems. Or the gold. Sure I could get more gold, but what do I care? It's not worth doing something unfun just to get more gold that I don't need. That would be stupid.
Heroics cannot bribe me anymore, so I must enjoy them. And the insane hopping miniature blood elf paladin with thunderfury, rocket boots, and a pretty dress, is going to damn well enjoy her heroics!
Here are the necessary screenshots. They're not very good. Warning: My UI is terrible.
The pygmy oil actually flips sex, so when I clicked it off, I was a male human. I used some more to switch myself again, male humans look weird.