Not sure if I fully understand, but would it make sense to cut your "cover" first to the size you need, cut it in half, then line up the two sides over the planter and mark where the hole needs to be?

Make a template using paper.

Look up "how to scribe"

Instead of plywood, I would use poultry fencing/chicken wire.

Jim's suggestion is best, I think. I didn't think about it at first, but covering the soil with a solid sheet of something would block rainfall to the roots, and maybe reduce air as well.

Maybe some lattice if you don't like chicken wire.

You might just do some research on simple methods to keep wild animals away from plants. IIRC its common to sprinkle various types of pepper around plants, but I don't know exactly what pepper might repel a cat. The idea is to make it distasteful but not harm the animal.

Bruce