Been there, done that!
Next time (and there will be a next time), order it 'Protein Style' Double Double with grilled onions. Ask for a fork and knive. Protein Style is wrapped in lettuce, no bread, disassemble, passing on the lettuce and tomatoes, you can fit the small patties and cheese in your pouch, cut into small bites, eating slowly and chewing well, it will stay down.
PS: Skip the Fries, and I always ask for water (Dont drink the water, but it stops the questions about not drinking anything)