Faithie the shear strength of my proposed solution will easily hold the 60 lb. battery. If you have a piece of some regular scrap 3/8″ plywood about the size of the unsupported section of the bulkhead laying around you could test it first.
Also, since you mentioned your battery was not secured to the galley floor, it is likely that the bouncing of the trailer during travels caused the battery to hop, turning a static load of 60 lbs into a dynamic load hammering on the galley floor.
If you decide to make a floor inside the galley module for the battery may i suggest going with your initial idea of a “1×1 stiffener” on the under side of the module floor screwed & glued into the galley module sides. Don’t forget to take pictures if you can, hopefully we can help prevent this from happening to more people in the future.