A beaut JB! Great way to mirror the book match with the divider.
MDF (and any other wood) will warp when veneered unless you add a "backing" veneer to the opposite side.
That said, if the panel is thin enough, any framing will hold it flat so boxes can often get away without the backing.
Since MDF doesn't have any grain for rigidity, The balance is even more crucial (same species, grain type, etc.)
Even the gluing process can add a bias.
MDF is nice to use because it is a great surface for veneer if done right, but aside from use in panels it doesn't have much going for it in the way of structural integrity.