If you have a screen top and he is rubbing on it you could do this (idea out of the blue, so not perfect..lol)
Find some of those "wipe-able" table cloth fabric. Where the printed side is that smooth, plasticky stuff.
Then cut a piece the same size as the inside of the screen top. Put your table cloth against the inside of the screen top (plasticky side towards the inside of the cage) and then STITCH it together with yarn !! The needle should go right through the fabric and also through the screen top, without damaging the screen.
Make sure you make SMALL stitches on the inside and larger one on the screen top. You don't want large stitches on the inside, just in case one might get loose and the BP would try to get into the loop.
Its kind of hard to explain and I made a quick drawing. Granted, its late, I'm no artist and its just a idea that popped into my head. So not sure it makes sense to you, LOL. I'm not that great at explaining.
English is my second language and when I get tired it "goes away"..
Well, here goes:
You can leave some round holes in the fabric where he can't reach to rub, for air flow![]()