I doubt you're going to find the plywood backer as a premade part. Just make your own out of exterior plywood and coat with epoxy.
A little lube, I like the white lithium aerosol grease, can probably get the control levers working properly. If not there are lots of different options from various manufacturers. Be aware though if you have the 5411 engine or any other that is shut down by pulling the throttle all the way back you have to stay with a two lever control. A single lever control is a lot easier to use but you would have no way to shut the engine off.