You could go old school and just add a pair of butt blocks.

I mean get some thin ply - 1/4" - cut to overlap the joint on both sides. Maybe 1' wide.
Glue and screw the ply to each side. The screws are mostly to hold the ply down while the glue dries - use Titebond 2.

The block on the upper side should not be so thick that you notice it beneath the mattress ????
It would be better if you could use some glass cloth/ epoxy to do the upper "block" in place of the plywood block but that means more materials, more time to cure the epoxy.

Good luck