The MDF cored ply is probably made for looks rather than strength.
It is just MDF covered with a thin veneer to be used in furniture and such.
MDF will suck up water like a sponge then swell and fall apart.
Go to as many plywood suppliers as you can and ask to see what they have.
The most important things to look for are:
Must have an 'A' bond (Waterproof glue).
Best to have equal thickness plys (Usually 3 ply).
Must have minimal voids.
It is good if it complies to a standard. I have found some 4mm plywood that is used for bracing in wood frame buildings. It is made to an Australian standard and has a stress grading of F22.
Get the best grade faces you can find 'A' is the best but you can use 'B' or 'C'if you select carefully.
Hope this helps.
Jon

: Are there other products I should consider? I was told of another ply with
: MDF? core, also avail in 1/8".

: Thanks