I treat a hard sided camper like I treat a house, cook in it, put food in it, BUT keep it clean by putting everything away at night and the garbage is taken out daily!! If you leave a open can of ham or salmon on the counter or in the garbage then you are asking for problems.
Issue that I have is the idiots that may have camped there before me and dumped grease or leftovers on the ground the day before.
I do also keep a can of bear spray in the camper just in case... a two legged or four tries to get in :-)
For a barbecue when done turn burners on high and let it burn off the food before shutting down. But the idea of using the bear box as well would work as long as you do not drive away the next day and leave it there.