Here is what I think in regards to this subject.

Glue ups are same princeple as gluing 2 planks up face to face.(heart to heart, bark to bark)

What I look for is balancing of final product, if additional strenght is required yes add MDO or other at this point I look at it like plywood core is balanced and has odd number of layers balancing each side out.

As per adhesive I would use what works on used combination of materials and per application.