Matt, I assume you brined your cheese, that would have given it a good kick start as a rind. On mine this goes away over time as salt diffuses evenly into the cheese.
My and most people's problem during the first few days is too much moisture. I use plastic Tupperware type boxes in my cheese fridge for ripening/aging and find the first few days I have the lid cracked an inch or so to let off the excess moisture, plus have two - three mats underneath to keep it up out of any draining whey. Then after few days as whey expulsion and evaporation reduces, I slowly close the lid until small leak. If you don't have a hygrometer, then I've found if lots of moisture on walls then too humid, if none then humidity too dry.
I used to use an insulated picnic box with freezer blocks to keep cool but found the condensation from the blocks gave me puddles of water and too high a humidity. Your cheese still being very damp after 4 days is not good, rather than drying at room temp my vote is to remove the wet napkins, less shock to your cheese.