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A varying "alpha" could eliminate that difficulty and could also resolve the helium problem in the early universe. When the Universe cooled after the Big Bang, a time came when there was no longer enough energy for the weak nuclear force to transform neutrons and protons into one another. This also set a ceiling on the number of helium nuclei that could be formed--but unless the strength of the weak force has changed, the amount of helium present just after the Big Bang was vastly more than such theories predict. If "alpha" changed so would the relative abundance of helium and hydrogen.
So it is an ill wind that brings nobody no good. The critical test will be the observations currently being made in Chile.
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