I originally made this puzzle just for myself and a few friends -- but for some reason Dr. Tom thought it would make a good MEOW. In fact, the metanism that he initially tried when solving this one inspired him to create an entirely new puzzle -- which doubtless you'll have the pleasure of seeing shortly! Thanks to Tom and my test solvers for suggesting a couple of tweaks that made this one a lot more fun.
Now: GO FIND THAT CAT!