Ahh, I see now what you're dealing with.
Hmm, why not take the new one and cut a notch in it's side wide and deep enough to fit the new rod, then simply "enclose" it with some circular plastic?
In other words, just glue a tube into the side of the box. This makes for clearance with the rod, but doesn't leave it open.
Just thinking out loud here. But if I'm picturing it correctly, just might work.
Probably only work if your intrusion into the box area is only a small amount. Like less than an inch or so. Anything over that and you're just interfering with it's carrying capacity.
But anything less than an inch should be easy to work with, and not take up so much space that it gets in the way of your contraband duct tape rolls. ;D
Paul