With shared dryers ... I'm sorry to say, the answer is pretty much no. If it was just a dryer that you were using, and no one else, the residue would disappear eventually - over time.
But, since other people use it and consistently put dryer sheets in there, you're out of luck. Sorry. I hate the dryer sheet residue as well, and never use dryer sheets. But, when I went to a laundromat, I just had to deal with it.
First special delivery - April 2010 :