Hi pancake--welcome back!
I use a combination of what you've said you try. I usually wrap in wax paper, then saran (very tightly), then throw the whole mess in a zip lock. I find a have better luck when I don't touch the cheese any more than I have to and also when I wrap tightly, getting out as much air as possible.
Thing is, I've had the same kind of cheese last a few weeks and last only a few days. I'm afraid that some of it is out of my control and due to the age it is when I buy it.
-A balanced diet is a cookie in each hand