Actually, I have a similar "game". While filling up one bottle under the sink, I unscrew the next lid to be filled and start screwing on the lid to the bottle that's already filled. I think I am wasting more time than saving, but hey, it gets me through it.
Right now I have a rat rack that holds six bins, four large and two of the extra large. I use these for nursing, weaning or breeding. I also have one of the 4' Christmas Tree Totes and two of the 3.5' Christmas Tree Totes. Along with a double stack ferret nation for the males.
I would eventually like to replace some of the totes with another rack, but I'd probably just end up filling those up too. It's hard for me to not hold a lot of them back.
As far as attaching the mesh to the tub, I melt holes in the tubs with a soldering iron and use zip ties to attach it. I rarely have issues with them chewing a zip tie.