[Son of Númenor]

I wonder (wildly) if Tolkien was not trying to reconcile the Elves' "karmic" debt for their deeds in The Silmarillion?

That is an interesting notion. I think another reason for Tolkien's portrayal of Frodo as having Elvish characteristics about him is that Tolkien, consciously or subconsciously, wished in this attribution to reconcile the world of the Silmarillion with that of the Hobbit. That is also why, I think, the Lord of the Rings starts off and lingers for a bit in the Shire, Bree, the Old Forest, etc. - Hobbitish places. As time winds on, the settings of the Lord of the Rings become less & less familiar-seeming to readers only acquainted with the Hobbit - Moria, Lothlórien, Minas Tirith, etc. - while the writing takes on a more 'heavy', dreary, mystical aura than it ever did in the Hobbit, beginning to somewhat resemble (in 'feeling', not so much in actual style) the prose of the Silm. An example of this that stuck out to me was this description of Aragorn:

...And taking Frodo's hand in his, he left the hill of Cerin Amroth and came there never again as living man. (The Fellowship of the Ring, "Lothlórien")

This had a distinctly un-Hobbitish feel, for me at least, & more closely resembled lines in the Silmarillion like

Yet in her choice the Two Kindreds have been joined; and she is the forerunner of many in whom the Eldar see yet, though all the world is changed, the likeness of Lúthien the beloved, whom they have lost (Silmarillion, "Of Beren and Lúthien"),

or

But in after days it was sung that Tuor alone of mortal Men was numbered among the elder race, and was joined with the Noldor, whom he loved; and his fate is sundered from the fate of Men (Silmarillion, "Of Tuor and the Fall of Gondolin"),

than any hobbit-related prose thitherto written by Tolkien. There are several other examples of this 'bridging' between two very different works throughout the Lord of the Rings - Aragorn's singing a part of the Lay of Leithian, the increased majesty of Rivendell & Elrond compared to descriptions in the Hobbit, the Rangers of Ithilien praying in fear to the Valar, the depressing poignancy of the Grey Havens, & other more subtle changes. Perhaps Frodo is the embodiment of this literary transition for Tolkien: a hobbit of the Shire who at first displays very hobbit-like mannerisms & sensibilities & interacts with other hobbits in a normal fashion, but who grows into a wiser & more Elvish seeming being as the book progresses from the cheery, charming atmosphere of the Shire to a darker, more mystically 'enchanting' piece.

I don't mean to get into allegory/applicability too much here, but the hobbits do tend to represent the 'little' or 'insignificant' people of the world, in which case Frodo's (& Bilbo's & Sam's) affinity for the Elves could be seen as akin (not allegorical!) to the downtrodden, the forgotten peoples of the world rising up against their oppressors, drawing on the knowledge & ideals of Enlightened theologians & philosophers of old (the Elves) in leading a revolution against foreign &/or totalitarian domination (both in the destruction of the Ring & the scouring of the Shire). To speak in less allegorical terms, the hobbits' (particularly Frodo's) relationships with & subsequent derivation of knowledge/wisdom from the Elves could merely represent the values & virtues that Tolkien felt were needed for some of the 'little' folk to lead the way to victory.

Blech! that all sounded allegorical, & a bit too reminiscent of Marx's Manifesto for me to be comfortable with it - but I hope you understand at least partially what I am saying about the possible meaning of the three hobbits' affinity with the Elves, & the reconciliation of the realm of the Hobbit to the world of the Silmarillion.