Well, you guys wanted me to run Deadmines. As you can see, I ran Deadmines. Many thanks go to Urse (Healer), Child (Tank), and Sneafoo (Noob Rogue of Doom) for 4-manning the thing with me. Urse was pretty overleveled for the place so healing was hilariously easy, but Sneafoo made up for it by starting the run at level 12 and aggroing Gruul from the pirate ship.
I went further than that, too. I didn't stop at Deadmines, I did Wailing Caverns, Blackfathom Deeps and Shadowfang Keep as well. I was kicking around the idea as soon as someone suggested Deadmines, but I didn't think I would manage to land a group for either of them. When I went out to the Barrens to get my Succubus (Angva) at level 20, that sealed the deal for me. I picked up the quest The Orb of Soran'ruk, and despite the fact that its quest rewards sucked, it gave me more reason to try and get the groups together. I put out a call to all of the various resources I knew, LFG and community chat channels (your server probably has a few good ones) and all of that, and managed to score a few groups.