I know you have a penchant for MDF, but in this case I'd be using 12 mm waterproof ply. Its not exorbitantly expensive, and is far more structurally sound.
Pretty cool design, I like.
Edit: when I say waterproof ply, I mean waterproof, not marine, there is a difference in both price and inherent qualities. Marine ply is predominantly use in boat building, where the structure will be or could be submerged. That's in an under the waterline application. Waterproof ply is more than adequate in any situation other than that.