Okay, so obviously no one person can clear out the admin backlogs by themselves (as it is, such a "I can do it all attitude is contrary to the wiki format anyway). However, I think I do have a realistic solution.
Something I try to do every night before going to bed is to address a backlog in some way, shape, or form. For example, one night I took care of a slew of I4s, while the night before, I took care of some I5s.[1] If every admin were to target a backlog and take care of maybe ten items and then went back to whatever else they want to do, we could start clearing out some stuff, but nobody would get too burnt out.
For example, Category:Images with the same name on Wikimedia Commons as of 10 April 2007 currently [well, when I first wrote this] has 129 items in it; just a dozen editors doing about ten deletions each would clear it out, no problem.
I'm not suggesting we co-ordinate our deletion efforts; that'd be a nightmare to set up. I'm just suggesting that anybody with a mop start chipping away at whatever backlog strikes their fancy. Like I said, just doing a handful of items every night before going to bed is easy, not particularly time-consuming (though anybody that wants to do 70+ items at a time is welcome to do so), and would go a long ways towards eliminating some of our backlogs.