What I have found in Italy is that the Parmesan and Grana is actually less hard than I have bought in UK cheese shops. In fact you can buy bags of big bite-sized, or two or three bite sized, chunks to munch on as a snack. Its not a "moist cheese" but definately less dry than I am used to from even the best UK cheese shops. As a result I would worry more about it "drying out" in the future than I have done in the past.
Yes, certainly protect from drying out further. Ours are just pleasantly "hard". But they keep very very well.
And of course, one week in plastic isn't going to hurt anything.