Your example of "should" is in the context of advice (present tense) rather than regret (past tense).
So how about: We were advised to take plenty of food to school / We had to take plenty of food to school / We were supposed to take plenty of food to school.
In my opinion, "had to" is the only option which effectively conveys that you definitely did take the food; the other two could suggest regret (in the same way as "should have taken").
Imagine a doctor telling his patient, "You really should stop smoking." The patient then talks about it to a friend and says, "I had to stop smoking on the doctor �s orders."