Definitely get shorter screws! When I mounted Burton bindings on my Nitro I "bumped" the base (thankfully I didn't do that to my Proto!). When I bought my Raiden bindings the screws where much shorter. I think Burton screws are too long for many non-Burton boards.
As for wiping down, you can wait until the snow as melted...
Where could I get shorter screws? Would I have to go to a board shop (none locally), or would sport chek or a hardware store stock them?