Jay, sorry to see the boards didn't survive the trip. They all look very nice. I think your assessment of the cause of the damage is probably right on. I'd guess it was a combination of heat, grain orientation, and not enough glue. What you've described and shown has indications of all three. I know from making some boards that didn't have the grain all going the correct way that sometimes they stay together, and sometimes they break. The heat and glue starvation would explain the other breaks.
Personally, I think I'd re-glue them where they've come apart and re-sand them if necessary to get them smoothed back out. For the hairline cracks, I'd probably see if I could work some Titebond II into the cracks and re-clamp. If not, you could re-cut the joints (you'd need to do all of them to keep the pieces the same size as each other) and re-glue. You may also find that now that the boards are back home where they started, the hairline cracks might close back up. (Still not great for wet food preparation, but the board could still be used for quite a bit of stuff.)
I've got a cutting board that did similar things as yours. It developed hairline to 1/8" wide cracks, including some split wood where the joint remained glued, but the movement broke the wood itself. The cracking happened a couple weeks after the board was made (and delivered to the customer
). A few months after I got the board back, the gaps had all closed so tightly I couldn't get glue into them. I don't use the board for anything other than decoration now, but it'd make a fine serving platter for cheese and crackers.