The hidden binary behind the Japanese numeral system

I've been inspired to write this after recent comments on my ire-provoking entry How NOT to reconstruct a protolanguage showcasing Sergei Starostin's posthumous reconstructions as exemplary anti-scholarship.

One important fact that everyone needs to know about Japanese numbers before blindly reconstructing Proto-Altaic numerals for themselves is that the entire decimal-based system shows a series of pairs in Old Japanese that "rhyme" through the use of internal vowel alternations. Please direct your attention to the folowing table:

fitö- '1'	futa- '2'
mi- '3'	mu- '6'
yö- '4'	ya- '8'

Everyone sees this phonetic/mathematic pattern crystal clear now, ja? The pattern is undeniable. We see two regular vowel alternations, one of i with u and the other of ö with a, by way of rounding and derounding vowels in one root to derive the other. This was written about in detail by Miller in 1967^[1]. However, it seems upon my brief Google Book search that it was remarked upon as far back as 1873 by Ellis^[2]!

So when poor ol' Mr. Starostin had reconstructed *ŋ[i̯u] "3" and *ńu- "6" (using both Old Japanese mi- '3' *and* mu- '6' as examples in the two cognate sets), I can only assume that he lacked adequate literature in his local library to have possibly overlooked this simple fact about binary vowel alternations in Old Japanese numerals. Oopsy daisy! Naturally, it shouldn't have to be explained that only one of each pair in the table above may logically ever be attributed to Proto-Altaic. We have to choose one. This is yet another reason why Starostin's online database of reconstructions must be taken with a big pinch of salt (or perhaps an entire truckload of salt).

UPDATES
(2010 Jan 28) I fixed the links to Starostin's reconstructions in his lingering database online. Someone wrote me lately that the reconstruction, *ŋ[i̯u] "3", shouldn't have brackets but they're clearly there in the database, only adding to the dubiousness of relationships claimed.

NOTES
[1] Miller, The Japanese Language (1967), p.337.
[2] Ellis, On numerals as signs of primeval unity among mankind (1873), p.50 (see link).