Ben,
I spent a week at a KOA in Salt Lake City a few weeks ago. I was surprised to learn from one person there that they had a monthly rate. It may still be more than you want to pay, but I think it ended up being in the order of $11-$12 per day. I don't know if the Vegas KOA has a similar program or not. When I pulled through there on my way back, they charged me $53/night! I had no choice with busted AC's needing electrical to hopefully get the bus cool!
Another possibility look for a storage yard in craiglist or similar. I would be you could find a "normal" rv storage facility for 1 month?