Sounds like a job for the good ol’ two-part epoxy. First, grab a solid, flat surface and spray a little 3‑M or J-B Weld on the top of each board where it meets the support. Let that go down, then wedge a small block of scrap wood or even a thick rubber gasket between the two pieces to keep the pressure steady while the epoxy cures—about 30 minutes to an hour is enough. Once that’s set, slide a thin strip of pine or cedar over the joint, press it in, and tap it lightly with a rubber mallet. That’ll lock the bond and give you that rustic look. If the boards still feel a bit wobbly, just double up the epoxy on the corners, or add a metal L‑bracket hidden behind a little cut‑out in the wood. And remember, don’t bother with a fancy wood glue; epoxy is the holy grail for this kind of “keep it together” job.