The cardboard is wrinkled enough that you may not get a good contact with either epoxy or contact cement. For this I would use Gorrila glue since it has great gap filling ability when it foams up. make sure it is well clamped or weighted so the glue does not spread it apart when it foams. I light mist of water on one surface will ensure that the glue gets a good foam on. Plan for foamed glue to come out of all of the edges, once cured it is hard to remove. I would make the ID of the ply cheeks smaller than the core ID to allow 3 or 4 bolts to run thru just to make sure it stays together for life.
