I would recommend getting another bin cage and filling it with a lot of bedding so he can have something more to do!
That would give him more space and a lot of burrowing space if you have the space for it.
I had my little hammy Lilo in the alaska cage a while ago and she always bar chewed. I resently upgraded her to the linnmon and she loves it, so the space really matters. Is the mesh on his cage on one of the sides or on the roof?