After thinking on this for a while, one thought comes to me about his choosing to die on his birthdate: it symbolizes, in a way, that death is no less a cause for joy as birth. Aragorn believed there was more awaiting beyond life on Middle-earth, and so for him, death was a matter of moving from one part of life to another. I think perhaps Tolkien used his choosing March 1 may have been a way to underscore that belief.