As long as the users see the pictures of un-flattened pizza-boxes, soft-drink-bottles, cans etc .. , they will fill the bins with AIR, and the bins will always be not big enough.
On the bins and the web-site, in the pamphlets and adverts in any publication produced, THE REFUSE HAS TO BE SHOWN FLATTENED, AND THE BOTTLES ALSO WITHOUT TOPS. To make the picture more relevant there is no need to show the whole flattened box: A corner with the flattening OF THE BOX CLEARLY VISIBLE drives the message better home. The top of a flattened bottle and missing top just the same. The space between the items does not need to be too big either.
Naturally a slogan&& can underline the visual information.
&& "Air is not refuse!!" or "Need help to stand on your box?" or "Have you flattened it ??"