LOTR only response:
Tolkien uses simile in a number of places to emphasise aspects of things and places, so that alone isn’t enough to exclude Elrond and his sons from the ranks of Elf-lords. The worst case for Elrond is that he is seen as straddling the line between races (Half-Elf). The respect he is shown by the Elves living in Rivendell, his age (~6500), the absence of reports of Men living in Rivendell, and the lack of fanfare surrounding the fact that Elrond married Celeborn and Galadriel’s daughter, all suggest that he is considered to be not just an Elf, but an Elf-lord.
Legendarium based response:
Of the Half-Elven, only two are reported to have chosen to be counted among the Edain (mortals): Elros and his niece Arwen. It is explicitly stated that Elrond, and his parents (Eärendil and Elwing) chose to be counted among the Elves. We are left without a clear statement about Elwing’s brothers (who are presumed dead) and Elrond’s sons. Other than that, there is Dior (Beren and Luthien’s son) whose status is unclear (born of two mortals, but accepted by Elves as king) and the rumours surrounding the line of princes in Dol Amroth although none of these are ‘officially’ Peredhel so they don’t appear to have been offered a choice of fate.
As Aragorn and Arwen’s children are accounted as Men, it seems likely that Dior would also have been. He wouldn’t have been the only example of Elves following a Man (Turin and Beleg) but as it isn’t clearly stated, there is room for argument.
I am still conviced that Dior's patronym not being "Beren's son" but "Thingol's heir" instead tell us something about his legal status. He is the only one having such a partonym as far I know. And that he is the real precendence for the possibility of a paternally human being being counted among the elves.
There's a really interesting, but subtle, moment in the Council of Elrond that you guys missed. (Forgive me if someone has already posted this, I don't keep up with the forum well and I'm perpetually several sessions behind now.) When Gloin asked the elf-lords about the Three Rings, the narrator says "The Elves returned no answer", but then Elrond immediately responds to him. What this tells me is that even though Elrond is counted among the elves spiritually, he is not counted as an elf socially/practically/etc.
There's another line in the Return of the King about Elladan and Elrohir which says "they are fair and gallant as Elvenlords; and that is not to be wondered at in the sons of Elrond of Rivendell". I know we're not allowed to talk about it yet, but I wonder if this is saying "they are fair and gallant because they are elvenlords" or "they are as fair and gallant as if they were elvenlords", meaning they are NOT elf-lords. There is definitely a simile comparing Elrond to elf-lords in the Hobbit, "He was as noble and as fair in face as an elf-lord", but if I remember correctly Tolkien hadn't decided he was half-elven yet, so maybe that doesn't count. Or is it "lord" that's the wrong term to describe him, not "elf"? How often is Elrond actually described as a lord and not as "master"? I don't remember.
I kept wondering about those textual eferences you have mentioned for long years and came recently to the conclusion that is Elrond is not an elf. He is a special category "Half-elf" even if he is little less then 3/4 of elvish descent.
But belong to neither of the three elvish tribes as those are inherited strickty paternally and paternally Elrond is House of Hador.
He is the son of the only surviving child of Dior Thingol's Heir who inherited his throne from is maternal grandfather (Thingol) via his non ruling mother (Luthien). As such Elrond would, like his granfather Dior, posses the right to be the ruling king of the Sindar via his non ruling mother Elwing. But like Dior he is not a Sinda himself.
His father Earendil was son of Tuor who has been adopted by Annael (a Gray Elf - Sinda) at birth and later declared the heir presumptive by his father-in-law king Turgon (Noldo).
Tuor is reported to have been rumoured to have counted among the elves. If so then his adoptions by the elves might be the reason to regard him as functionally half-elven. He was with humans only from his 16-19 year when he was kept as a slave by the Easteling as far I do remember. So just 3 years of his puberty. Otherwise Tuor had no contact with humans whatsoever beyong seeing his cousin Turin from afar in the woods at one time.
Earendil has been raised in a Noldo city of his maternall grandfather but was still paternally House of Hador, so are his sons and his granchilden. As such there are all half-elven oeven if by blood the latter ones are almost elvish.
As such Son's of Elrond are counted as House of Hador as Aragon would be were he not as he is speciffically House od Elros.
A such they are descibed as elvenlords-like and not as elvenlords simply. Makes total sense if you consider the importance of agnatic descent for the elves.
As such if Aegnor and Andreth had a child, if would have been a Noldo of maternally human descent but by default an elf imho.
