Hoovers are great! But Dysons are too! Is your Dyson clogged?
I don't have a recommendation on a Hoover model, but an idea for the cat box. I also have a cat that throws litter everywhere and I finally put down a commercial grade throw rug under the box and that has helped to contain most of the litter. It also helps a great deal with clean up! The rug is like like the ones that convenience stores use at their front doors and in front of their soda fountains. Cost an arm and a leg, but last forever.