I haven't been on here for awhile but will answer here since it remains unanswered.
Most rabbits are fine with fleece, but they will usually chew holes in it. Remember with a rabbit, it is best to skip the second "c" in C&C. The coroplast is very slippery and bunnies can't get grip with their furred paws.
When I used NIC or cube cages (rabbit version of C&C), I used rolled linoleum for the main base and was able to use carpet remnants on the upper levels. Of course, this assumes bunny doesn't chew & ingest the carpet (mine did not).
I'll see if I can attach a pic of my old cube cage. I now use a cage made out of an old oven cabinet. The cage door is left open all day.