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I didn't know there was such a syndrome as "Searching for Deeper Meaning in Anime." Personally, I don't look for meaning; I just see whether it exists or not. In Elven Song, it was there (maybe not philosophical), and the action was also great. As for Evangelion, I watched two full-length movies; one was a compilation of scenes from the series (for those who don't want to watch the whole series), and the second was an alternative ending. I give Elven Song a higher rating overall. The full-length movie felt overwhelming, even though I can't pinpoint exactly why (probably too much unnecessary information), but it did. And the second thing I didn't like was the strong emphasis on religion. That's my opinion...
P.S. The average Japanese person will find philosophical meaning in a simple stone.