This is much smaller than yours but I like multi purpose items. I use a small cooler to store the cooking tools. You can always dump everything into a bag and fill the cooler with ice if you need to change applications. Probably don't want to do that with a wooden or uninsulated plastic box.
In this little igloo I have 2x propane bottles, bottle top burner, lighter, dish soap, bottle opener, game scissors, spatula, filet knife, flexible cutting board, small regular cutting board, ceramic coated steel cup, small cook pot with lid, medium cook pot, ziplock bags, plastic utensils, olive oil, crab boil, jar of packet condiments, and my spice box.