Do teams checking in two planes need a separate measurement box for each plane, or can a single measurement box be used to verify the dimensions of both planes?

No, teams do not need a separate measurement box for each plane. You may if you wish, but one is sufficient. Per rule 2.b "Teams must bring one or more Measurement boxes..." One box will satisfy this requirement, the sentence does not require more, only allows more. Rule 5.d is consistent, competitors provide measurement box(es), but may be as few as one for both planes.