I can happily confirm that the hamper arrived in perfect condition! We loosely wrapped the hamper with bubble wrap, and as suggested by Giggleswick, placed it into the B&Q storage box linked above by fluffymitten, with gaps filled with the foam peanuts that came with the hamper. The box was then secured with Gorilla Tape, and then wrapped in plastic at the airport. The hamper was filled with clothes and blankets, and the actual food items were in our traditional luggage.

No trouble at all at bag drop, transit, reclaim, or customs. Some scuffs and holes in the plastic wrap, but ultimately even the storage box is still in good enough condition that I think one could get away with returning it to the store (were one to be arsed to bring it back).

Thank you everyone for all your good thoughts and advice! Happy holidays!