I am sure he would love some more things
They like using all of the cage when they have other places to go
Maybe get some sandpaper too! I keep some handy and check any wood items for splinters. A bit of sand paper can smooth it in seconds. Plywood should be fine - it you can find plywood that's non toxic it helps - there is a thought that the glue in plywood can give off fumes but I have a plywood shelf and never had any issues - just get the best grade of plywood you can. Or you can just use a piece of plain pine wood - pine is ok when in solid pieces - it is the wood shavings that can be unsafe (unless they are kiln dried).
It's a rare genetic condition I think
Glad he found you!