I'd really encourage you to use Quick Set JB Weld. It won't take any longer than the Gorilla glue and will last your trip and longer.
If you can remove the lid and take it inside for repair, it will make the repair process much easier, although the hinge bracket
reassembly can be a bit fiddly with the tiny domed nuts. The bracket screws are not that difficult to strip, at least they weren't for the P.O...
For the repair, use longer screws as shown in the pics to give additional purchase below the break in the towers. First assemble what you can, including
the broken pieces if possible, onto the plastic towers and assemble with the longer screws. Remove the screws, lube them with grease
and assemble again. The grease will allow you to remove and replace the screws once the epoxy hardens. Place the lid so the towers
and posts are vertical. Mix up the quick set epoxy and and coat liberally around the tower and posts where they attach. You may
need to add more epoxy while it's hardening, as it will flow down to the base of the towers, but the quick set epoxy will set quick
enough to allow a good coat around the vertical surfaces..
Good luck with whichever choice you make. Hope the weather will allow you to choose the epoxy.