With fleece you won't have a mess outside the cage, but you'll be able to see the poop. How many piggies you have? Maybe litter train them?!
I use fleece, but you have to carefully clean the washer & dryer after you do piggie laundry. It is also quite tricky to get it not to smell. You'll have to change it at least 2 a week.
I think you said that your cage is big. I beleive is not a C&C cage, so What is the bottom of the cage? Wood? You should have a plastic bottom (coroplast). That needs to be clean too.
There are always options for the cage that'll fit your needs. Tell your parents that you are going to try other things. They might give you another chance...
If you tell us exactly what you are doing, we can tell you what might be causing the smell. Pictures are good also!
