because i am lazy and have 10 chins this is the method I use to cut down on time.
every night i do a clean sweep of their cages. remove all poop, hay & shavings tossed from their litter boxes. i do use litter boxes in every cage and have found that over time they use them more & more. I dump shavings every other day with the exception of my pair they get dumped daily. sometimes i add a small handful or turn the tray if they seem to pee in one spot. for 9 cages this takes me a minimum of 30 - 40 minutes but this does involve at least 2 to 4 chins coming out. I usually take 1 chin out and clean his & 3 other cages (or two fn towers). than i move over to my more needy group and take out 1 and clean 2 cages, take out another & clean 2 cages and finally my Richie comes out and i do his cage, clean up, get ready for bed and then put him back.
the one trick i learned in some of the cages is to lay an additional piece of fleece where they pee in those cages that they do not exclusively use the litter box or my rescue who dumps her water dish. i get smaller pieces of fleece and fold them and lay them in the area where they pee. I usually change this piece almost every night. it has really cut back on the odor as well as keep those cages cleaner and easier to maintain.
One time per week I do a complete clean, where I remove the fleece, vacuum under and around the trays, wipe the trays with either clorox wipes (cause im lazy!) or spray my organic sun & earth spray. i lay new fleece, wipe down all shelves, housing, marble, etc.
I try to break this up into 2 nights, 2 towers one night, 2 the next plus rescue. sometimes i do 1 tower a night.
I shake all my fleece at once. usually try to store it in a big bag so it doesnt smell up my laundry room. I agree when there is snow on the ground or it is freezing it really is a pain. i have been known to get a big black garbage bag and shake them out in there during snow storms!!
hopefully that all makes sense.