Overhead Cabinet Separation '67 Safari

[airdrmr]

We have had our '67 Safari for a little over a year now. Since we've had it, we've noticed a slow separation of the overhead cabinets above the gaucho from the interior wall. We believe the separation started with the curved end panel next to the fridge, where possibly a rivet came loose (?). Most likely the PO was storing something too heavy in them. Now the center overheads are starting to sag and we've noticed a couple of cracks in the thin wood holding them together.

Wondering if anyone out there has ever had this problem, and how to best deal with it. I'd like to save the cabinets, so I'm looking for suggestions on the best way to repair them. Would it be best to remove the cabinets to repair them?

My husband is pretty handy, so he can do the work, just need some suggestions on the best way to tackle this project. Thanks for any suggestions!