Unless the bars are somehow different on the new cage I don't think it's going to help much.
I made this diagram as a suggestion on what you might do with your existing cage. You can find stainless steel L channel and bar at a hardware store. To build this you need a drill, a hacksaw, and a file to make sure the sawed edges are smooth. It is a suggestion and I don't know if it can cause a problem or not. Take care to set it up so there are no pinch points or places where chinchilla feet can get caught if you go this route.
You can cut everything to the sizes you need to support the heavy accessories or even bolt the accessories to the new structure.