Managed to find a strategy pretty quickly: begin from the outside, opposite of the direction you want the cat to go in; then fill until you have 1 exit in that direction and begin to fill in the exits while the cat travels to the one open route, and when it's one step away you close it. You then have many more moves before the cat can get back to open area, in which case you can repeat until you have a closed loop.
I eventually found a strategy of basically trying to fill every "even" space around the edge, and then only filling in the odd ones when the cat was 1 space away from entering the edge-ring. This would allow me enough time to enclose the entire board, after which trapping the cat into a single space is just a matter of time
The Angel (cat) in this example is incredibly naive which made it easy to realize that strategy would work. Would definitely make for an interesting 2 player game!
