I, too, would keep the fuel tank full when parked/stored. I try to fill up whenever we are parked in storage for a while.
Currently, our coach is going to be parked for 6-8 weeks. I know the OP is talking about a gas unit but I never put anything in our diesel tank (not recommended by manufacturer). In about four weeks, I'll take the motorhome out for a 30 minute run to warm everything up. We never winterize as we use the coach about every month.
Mr. Darius, can you take the motorhome out on a monthly run for 20-30 miles or so to warm everything up? That way, the tires can get the heat they need to keep the 'emollients' circulated through the rubber.
Safe travels,
MM.