According to my instructor's notes, in situations such as
Most of that rack of paperbacks is/are trash,
where the prepositional phrase contains both a singular noun and a plural one, the choice depends on which noun the verb is really acting on. The notes say the plural is correct in this example because the sentence comments on the books, not the rack.
Another example is
Most of the box of cookies has/have been eaten.
According to the notes, have is correct because the cookies are being eaten, not the box.
This approach results in sentences that do not sound right to me. It seems to me that the singular conjugation would be correct in both examples. My reasoning is that the "of the box" is essential and can stand alone, unlike "of cookies." You could say "most of the box has been eaten," but removing "of the box" only works if you say "of the cookies" instead of "cookies." It does not make sense to say "most of cookies have been eaten." This leads me to think you should say "most of the box of cookies has been eaten," and only use the plural if you are saying "most of the cookies have been eaten." It just doesn't sound right to say "most of the box of cookies have been eaten," which immediately creates a sense of conflict between the plural have and singular box.
Additionally, the reasoning that the verb's agreement is a result of determining which noun the verb truly acts on does not work as well in some situations. For example,
The team of players is/are eating lunch.
Neither team nor players has any precedence over the other, and it makes perfect sense to say either one is eating. You cannot determine which noun the verb is really acting on.
A similar example can be found in this question. The answer says it is ultimately the writer's choice to emphasize one noun over the other.
Is this the best answer to this situation? It makes more sense than my instructor's notes, but it still seems that the singular conjugation sounds better. How is subject-verb agreement supposed to work in cases like these?