Given the often idiosyncratic nature of Homeric allusion, both of the foregoing are more attractive than the idea of an independent tradition, which Homer could expect his audience to understand.
Both Iliadic allusions, though, also seem problematic. Particularly troubling is the reference to Agamemnon's rejoicing (Odyssey, 8.78). This does not work very well in Iliad, Book 1, and it would be even stranger in connection with Book 9.
Another passage therefore needs to be brought in, viz., the "reconciliation" between Achilleus and Agamemnon in Book 19. As is fairly well known, this scene, as it refers (Iliad, 19.140-141) to the gifts which Odysseus offered to Achilleus, serves to anchor the Embassy of Book 9 firmly in the Iliad. Book 19 also qualifies as a quarrel between Achilleus and Odysseus, since they have very different views on whether they should eat before fighting the Trojans. Despite this difference of opinion between two of his major warriors, though, Agamemnon could still be regarded as rejoicing on this occasion, since with Achilleus' return there is indeed an expectation that Troy can be captured.