I am making a router tabletop out of 1/2" corian. The Insert is 3/8",
leaving 1/4" of corian. That might be strong enough, but I sure don't want
to chance it. I would like to reinforce the bottom. I can glue plywood or
more corian to the bottom around the cutout to strengthen it.

Would plywood (1/2"?) be adequate, should I use corian, or something else?
Is epoxy a good choice for the glue, or maybe polyurethane?
Is glue adequate, or should I work some bolts into it as well?