Like Serendipity's idea, instead of shelves I tied these mats to the inside of the roof on one of my cages.
I wondered if that could help you. Serendipity helped me a lot when I was setting up my cage for an elderly hamster, it gives them a bit of cover still, but in your case it may help prevent monkey barring.
https://www.zooplus.co.uk/shop/small...es/mats/204595