Years ago when Evaporust showed up they had a customer photos page on their website and some guy cleaned the bottom of his car using a small fluid pump that recirculated the Evaporust that he was using to wet down the bottom of the car with. He had a rubber hose hooked up and just moved it around every so often. He had a plastic sheet on the floor to catch the fluid and re-direct in back to the pump. Maybe you could build something similar on a smaller scale and pump a rust remover into the void space?

I think they make an Evaporust gel that goes on like paint stripper. Maybe you can get that up inside there and then rinse it out?