Here's an interesting point, from the original post:
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The fact any Fibonacci sequence converges to this ratio is not what makes it so significant.
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I would venture to say that this is exactly why the ratio is significant. Think about it from a statistical point of view. That any system which is governed by Fibonacci ratios ultimately converges to Phi, regardless of which Fibonacci sequence is used. Imagine for a moment that the mechanics of life are based on Fibonacci sequences. That is, cell differentiation, protein production, cell division, etc. are all based on Fibonacci sequences. Then, it doesn't matter how many origial cell you start off with, or which cells differentiate first, after the system has reached steady state, any stuctures associated with such mechanisms would have ratios correlated to phi. Remember, also, that Phi is a ratio based on the Fibanocci sequence, whereas sqrt(2) and e are not ratios of common geometic sequences (at least, not that I know of. I'm no math major). Everything that people have been looking at are ratios.