It might work. I haven't try it tho. I had a similar idea ones but instead of old plain MDF, I was thinking of using the product which name escapes me right now (I can find out its name if you want). It is a laminated MDF and Ply in 5 layers (top, bottom,mid MDF and Ply between). Cabinetmakers use it on special occasions when rigidity is of up most importance. It's the perfect material for your project, easy to work with and finish. Price might be an issue but I do not believe that it is more expensive then Baltic Birch (void free) Ply. If I had to guess, it might cost somewhere around $80 per 8'X4' sheet these days. (year ago it cost $60).
I hope it helps
Mariusz
