Synonymic Sustenance
Answer: ROLL OVER
Alan Abraham, Robert Trosten, Summit Wei

The puzzle presents us with a whole glut of information on a bunch of boxes, but the flavortext implies that only one piece of it is relevant, and the rest can be ignored. Furthermore, the words "Just One" in the flavortext are capitalized, cluing the party game, where a player has to connect several seemingly disconnected clues together with a common thread. The word "synonymic" in the title confirms this connection, since synonyms are pretty close to what needs to be done here. Since this is a metapuzzle, the most natural thing to do is to try to connect the feeder answers together in this way.
The connecting word is DATE: One's girlfriend is their date, a date is a type of stone fruit, "until now" means "to date", a meet-up can be described as either a rendezvous or a date, and something antiquates when it dates, i.e. goes out of date. From this, we can see that the only useful piece of information in the boxes is the expiration dates on each box.

Because the flavor mentions the US Collins COBUILD dictionary, we should look up our words in there; it seems most promising to look up the word DATE. There are ten definitions listed. Also, the years on the boxes seem suspicious, and upon applying A1Z26 to them, the message is MONTHDEF. This implies we should correlate the months on the boxes to the definitions in the dictionary.
Indeed, the eight boxes have only five unique months among them, and each of the five corresponds to one of the definitions of the word DATE, along the way that it is connected to one of the feeders.
Definition 2 is an "appointment to meet someone", which is the answer RENDEZVOUS.
Definition 4 is "someone with whom you are having... a romantic relationship", which is the answer GIRLFRIEND.
Definition 5 is date as in the fruit, so it is STONE FRUIT.
Definition 8 refers to something going out of fashion, so it is ANTIQUATE.
Finally, Definition 10 links to "to date", which is directly a synonym of UNTIL NOW.

Now that we've made these connections, we still have yet to use the days on the food boxes. For these, we index into the associated words to yield the answer, ROLL OVER.


Author's Notes

This puzzle originated with the concept of the boxes, which turned out really nice -- thanks to Alan for making the art for the puzzle. The initial title of the puzzle is "Flavor Text", which I really like as a pun, but was changed to add an additional clue for the break-in as well as to steer away from the red herring of using the flavor text of this puzzle or other puzzles for extraction.
The final answer to the puzzle is meant to tell you to go to sleep; I really hope hope people actually did this during the hunt.