I haven't mentioned it yet, and no one else has, but... You guys are building Ice Boxes, right?

Once you can build 2 Football Helmets, 2 or more Log Suits, and a Spear, you can take on at least a couple of the clockwork chess pieces.

With a bird in a cage... you can feed it cooked monster meat or monster jerky at any level of spoiling and get fresh eggs. When the eggs start to spoil, you can cook them on the fire and feed them back to the bird for fresh eggs. Hence, a spoilage work-around for at least one food.