“It hardly makes sense for Homer to use any word that his audience could not understand, if his performances were public.”
Actually, it’s not unlikely that there were some words that would have been unintelligible to early audiences, and perhaps even to whoever composed the poems themselves–words that had become embedded in formulas in the traditional language of the Homeric poems at an earlier stage in the tradition and were no longer meaningful when the poems were composed (as well as words and forms alien dialects). The formulas themselves may well have meant something to performers and listeners, but not necessarily what they originally meant. As early as the sixth century BCE, the Greeks were struggling to explain obscure words in the poems, and, often as not, their explanations were wide of the mark to the extent that the meanings can be recovered today by historical linguistics. Despite their inability to understand every single word, the Greeks continued to enjoy hearing performances of the poems and reading them, just as we can today without being able to explain everything.
“If anything it’s a u-stem adjective in my opinion, should this etymology be accurate, after the intervocalic sigma disappeared.”
This explanation wouldn’t explain the strange forms of this word, e.g., θεοὶ δωτῆρες ἐάων. The feminine genitive plural would have to be ἐειάων or perhaps εἰάων, wouldn’t it? And that wouldn’t be metrically possible.
LSJ:
Ep. word freq. in nom., “ἐῒς [this is an obvious mistake in the on-line version] πάϊς Ἀγχίσαο” Il.2.819, etc.; once in acc. “ἐΰν” 8.303; neut. always ἠΰ (v. ἠΰς) (εὖ only as Adv.): irreg. gen. sg. “ἐῆος, παιδὸς ἐῆος” 1.393; “υἷος ἐῆος” 15.138, 24.422,550; “ἀνδρὸς ἐῆος” 19.342; “φιλότητι καὶ αἰδοῖ φωτὸς ἐῆος” Od.14.505; always at end of verse (exc. in Od.15.450): freq. with v.l. ἑοῖο, as Il.18.71: irreg. gen. pl. ἐάων good things, good fortune, 24.528; “θεοὶ δωτῆρες ἐάων” Od.8.325; δῶτορ ἐάων ib. 335, h.Hom.18.12, 29.8, cf. Hes.Th.46,111.
It only seems to exist in a restricted number of forms in specific formulas fitting specific metrical slots.
By the way, the American Heritage Dictionary is the work of Calvert Watkins, who was one of the most outstanding Indo-European linguists.