Cage cleaning time for me is 5 Minutes. I kid you not. (this obviously does NOT include washing the bars or pan).
This is achieved by having a layer of newspaper, then a layer of fleece. Simply lift the cage off the pan, roll up the fleece, shake it into the bin, put the newspaper in the bin, replace with new paper and clean fleece. Voila. 2 Minutes tops. Another couple of minutes to wash their plastic house and litter box and perhaps replace hammocks. Sure, every so often, you´ll need to clean the cage itself (i.e. bars and pan) thoroughly, and that takes about half an hour, but other than that, it´s no issue.
Maybe your cage is just poorly designed? Check out Martins Cages here:
http://www.martinscages.com/products/cages/rat/ , I´ve been VERY happy with mine so far (make sure you get the powder coated ones).