This is my solution to the problem- a pair of hose pinch-off pliers, and will work for anyone that has a flexible drain hose and has access to it. My FWT is under my bed so the drain hose is a piece of cake to get at. I keep the pliers right next to the hose so they're always handy.
The ones I have (pictured above) are made by Lisle, Model# 23000. Any good auto parts store should have this or a competitor's brand in stock.
One word of caution: I would not pinch off the drain hose until after the tank is full to ensure there's a path for air to escape while filling the tank.