Chinchillas need shelves. It's funny I just created a guide to making shelves about two days ago. Here is a link:
https://www.facebook.com/photo.php?fbid=1459579484355695&set=a.1389112151402429.1073741828.100009109720588&type=1&theaterI agree there's a lot of conjecture on wood. The fact is all wood has a certain amount of toxicity because of the resins it contains so I imagine you'll have a lot of false positives out there. I use white pine since it is common and it is standard practice in the industry is to make shelves and toys from it. Aspen is also common and acceptable. Apple wood is also commonly used in sticks and branches. These woods are proven to be safe and are soft enough to encourage chewing. Avoid cedar or anything that has a strong scent.
The shelves I made are all plain white pine boards. I am using a couple of different widths. Please do experiment and build things. I'd love to see your designs. Just keep in mind chinchillas are very active at night when you are asleep and sleep mostly during the day. They are so active that if there is a way to find trouble they will find it so be very careful when designing your toys so there are no pinch points or openings they can get their head or limbs caught in. The hay ball is a good case in point. If you use chain only very short sections should be exposed. I strongly recommend replacing any plastic in the cage with wood or metal. Plastic when ingested is a known killer of pets by bowel obstruction.
I'd start with wood shelving, maybe a tunnel or half a tunnel. Hanging toys are popular with my pets. Pumice is something that can my chins like. Also have some loose things that they can grab and move around. Mine will carry or drag toys around the cage.
As far as a wheel goes you may want to obtain a better wheel that uses ball bearing such as the chin spin. Diameter should be around 15" This is a bit expensive but it doesn't sound like the other wheel is working. Maybe you can weld or modify yours to see if you can make it resistant to being pulled apart. Perhaps you can use a washer, heat the wire, then crimp it over the washer.
I'd be careful about movement like motorization because chinchillas are easily frightened.