1) get some 3/4" particle board or plywood from Home Depot
2) rip a 3" wide and 12" wide strip long enough to span both halfs
3) position 12" strip on a flat surface amd shimmy it so that it would lie flat and parallel to the ground. Use a long carpenter's level, at least 3' long.
4) Glue(Thick CA with kicker if you like) 3" strip to the side of the 12" strip at 90 degree angle. Make sure the top of the strip is parallel to the ground
5) Position halfs so that the trailing edge sits atop of the 3" strip. Weigh it down so it does not move
6) shimmy halfs near the center seam so that the tops align and halfs are pushed up against each other
7) epoxy 1" wide tape along the seam. Let it dry.
flip the cores and repead steps 5 through 7.
Done.