Naio, that fuzzy layer serves a couple of purposes, along with insulation for heating and cooling purposes it also is a noise dampener. Also living in a closed container that size, moisture from your breathing keeps the humidity higher than what would happen in a vehicle only occupied for a couple hours a day.
Depending on how you are doing your build out, you may want to cut the flooring and build in the permanent parts, framed base for bed or cabinets with maybe just a rubber sheet bottom. And after everything is fixed in place, cut and relay the factory type flooring in the areas which will be open. It should help keep you more comfortable and quieter, and maybe you can keep those open areas removable so you can literally hang them out to dry occasionally if needed.
Happy motorin