As for Aragorn interrupting the Fall of Gil-Galad, JRRT explains in one of his letters (incidentally the very interesting letter where he comments on a LOTR movie script he had been proposed in his life time):
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Aragorn did not 'sing the song of Gil-galad'. Naturally: it was quite inappropriate, since it told of the defeat of the Elven-king by the Enemy.
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The tale of Beren and Lúthien in turn was one with a glorious ending for both, definitely also more appropriate for Aragorn's personal situation, using Beren as a role model.