In QS, contemporary with the Lhammas, Tolkien had *all* the Danians eventually go on to Beleriand, without leaving any kin behind; and (consonant with the Lhammas quote) used the term Pereldar 'half-Eldar' for them. (Thus of course when the Lorien chapters were written the Elves of Lorien were seen as Avari save for Galadriel herself. In this connection Imrazor+Mithrellas isn't counted in the Appendices as a Man-Elda marriage. But under the later conception this can be regarded as a needed correction overlooked, like 'House of Finrod.'
In 'Concerning Galadriel and Celeborn' T says that Galadriel in Eregion had
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come into contact with the Nandorin realm of Lorinand on the other side of the Misty Mountains. This was peopled by those Elves who forsook the Great Journey of the Eldar from Cuivienen and settled in the woods of the Vales of Anduin.... Many Sindar and Noldor came to live among them, and their 'Sindarizing' under the impact of Beleriandic culture began
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No suggestion of Avari being present in the mix.
At any rate, for the purposes of this discussion, it's enough to observe that no named Avar ever appears, so it's silly to look among them for a 'great' Elf.