Maybe you could use Coroplast (sp?) as the tray support. It is a fluted polyethylene and resembles cardboard in layout. I've only used 1/4 stock, but perhaps there is a thicker version, or you could double it up. For long term storage, you should also consider Marvelseal to seal the crate, to protect against the wood off-gassing.

I have also read somewhere that if you have questionable materials in a long term storage crate, it is best to allow it to vent. I have not done this, but imagine there are others that have and can chime in too. I would maybe place shims between the lid and gasket before mechanically tightening the closure bolts; this will leave a space so that any off-gassing won't build up over time.