I have a Char-broil gas cast iron grill.  This is one of the style where the flame is under cast iron pans filled with lava rocks rather than cooking the food directly.  Works great for when you don't want to bother with charcoal.  But I digress.  My question is: I think this type of grill would make an excellent smoker, and has anyone tried doing so before?   were you able to keep it at the right temperature?  How? how much wood chips did you use?  Did you soak them? did you try to seal it to keep the smoke in?  again, how?  
In either case store the cheese in the liquid it came in, transferring it to a clean container and covering well. Feta lasts reasonably well, but mozzarella only keeps well for a couple of days. 