I'm experimenting with using double-walled corrugated board rather than binders board since it has strength but not weight. The board surface is easily marred but with the book cloth adhered it seems pretty solid. I'm going with a telescoping design, that is a smaller tray that has a separate slightly larger lid that fits over it.
What I'm not sure of yet is the design of the lid. The base is too big to make a lid from one piece of board, so I will have to cobble something together. I'm also considering experimenting with a polyester lid so you can see into the box. Nothing will be stored on top of this box, so having a sturdy lid may not be an issue, but would it provide enough protection? More thought is needed. Luckily the next few days are chock full of meetings, so I'll have time to mull it over.