You know you just put one ball through the hoop at a time and then slide his cock through? That’s how you’re doing it? It’s not a squeeze them all through in one go effort. (Just checking! lol)
The largest size on the CB6000 models is a couple of inches, that pretty wide, and it fits together in two pieces so you don’t have to squeeze through anything. Have you tried those?
Something like the 50mm ring on The Arc cage that we reviewed recently is pretty damn big because of the shape of the ring, I’d give something like that a go too. You could send a message to the guys who run that site, they’re very helpful and might know more. Otherwise you’re looking at a custom cage which is super expensive but they can make them whatever size you want.