If you're concerned about noise, foam or cork roadbed would be your best option for sound deadening. Cardboard is unlikely to help, and it wouldn't stand up to scenery glues in any case. If by drawer lining, you mean that expanded rubber mesh stuff, that might work.
Thing is, I have two observations: first, I'd get in there and deal with that bowed surface. Add some support underneath; if it's wood, make sure the grain is perpendicular to what's already there1. Secondly, though, it doesn't really matter if there is a slight height difference between the two. If the sound deadening is more important, then by all means add the roadbed. Scenery will camouflage the different heights.
Thing is, I have two observations: first, I'd get in there and deal with that bowed surface. Add some support underneath; if it's wood, make sure the grain is perpendicular to what's already there1. Secondly, though, it doesn't really matter if there is a slight height difference between the two. If the sound deadening is more important, then by all means add the roadbed. Scenery will camouflage the different heights.
