I installed the transom core by applying a bed of epoxy that I had thickened with Cabosil and then used a notched spreader to apply uniformly and put grooves in it. After that I temporarily wedged it from the inside while it used dry wall screws to tighten it against the outer skin and hold it in place while the thickened epoxy set up.
A week after the core was installed I finally had time to start glassing the inner skin.