He doesn't bother the rim -- the frame is heavy-gauge wire wrapped with raffia. He attacks the soft stuff on the sides, all in one area so far.

And even if you can’t wrap each row independently you can group wrap. Find colors that you like and have fun with it.

I zoomed in. You can still use material there! Just wrap around the areas he is chewing on. Check online on Chewy for bitter apple spray. It’s supposed to deter stuff like this.