Use compact food--for example couscous instead of pasta (it's the same thing, actually). If you absolutely must have pasta, take a hammer to it!

Repackage commercial freeze-dried food into ziplock freezer bags; be sure to label the bag with a permanent marker. Remove as much air as possible (try a straw). Some like to put a pinhole in the bag next to the closure so more air can be removed. Don't use vacuum packing, though, because it turns the food into a solid brick. You want stuff that squashes to fit the space!

Put the first two days' food on top so you don't have to unpack the whole canister and then try to repack it while it's full.

The first day's food (lunch and dinner) doesn't need to go in, because you'll be eating it before nightfall. However, leave room for smellables (toothpaste, sunscreen, etc.) the first night.

Pack a thin layer at a time and squish really hard after each layer to force the food into every crevice.

It's amazing how much you can get in there if you use compact food and squash hard! However, there comes a point where you need either a larger canister or a second smaller one. 12 person-days is a lot for even the largest canister. I've done it (4 people for three days in the largest Bear Vault), but two of those were children aged 6 and 8, and I had to repack the Bear Vault three times to get everything to fit.