I wasn't trying to be clever about the comment on Copydex.
True contact adhesive (some variants also called 'Barge') do not 'wet' the materials they are applied to. Its a neoprene rubber compound that creates a chemical bond between two glued surfaces. It is normally used for large areas of non porous materials such as bonding laminates to kitchen counter tops. But it's also used a lot for glueing foam together by cosplayers because it simply doesn't fail and it instantly bonds difficult materials, but remains flexible!
The rubber compound in a contact adhesive is mixed with a solvent to make it liquid in the tin you buy it in. You apply a thin coat to both surfaces and then let the solvent evaporate for a few minutes, and then introduce the two DRY surfaces to each other where the grab is instant. You get one chance.
Copydex on the other hand is a trade name for a WATER based latex glue. It cures by the water in the glue evaporating. It works by being absorbed into the materials it is bonding.
The upshot of all this is Copydex will warp your mdf boards. Contact cement will not. I have bonded sheets of 3mm hardboard and 2 mm MDF together without ANY distortion.
With the right glue you really wont need a 9mm board. (you may want a thick board to support the mass of the items glued to it, but that's a different issue)