underpad for fleece cage

A couple of years ago, I built my boys a 2 x 4 grid C&C cage, and a run around pen thats another 4 x 4 grids in addition to the 2 x 4 living space. I've been using towels, training pads and fleece for bedding in their cage area but I've recently gotten it into my head that they would love a "squishier" for lack of a better term, bedding under the fleece. I bring them onto my bed with a feather duvet and they absolutely LOVE walking around on it and hiding in it. They never poop or pee on it and they just flake out when I bring them in. I kind of want to use a 1" thick foam mattress topper underneath the fleece and training pads, but the foam rubber scares me. Anyone have any better ideas? My pigs are my babies and the thought of anything happening to them absolutely rips my guts out so safe alternatives are what I'm looking for, please!