I figure a small physical constant jog could easily make the difference between intelligent life emerging, and it not doing so billions of years later.

First, that is VERY different than the design information being in the constant, but not in the genome. (you could more validly say that the genome is what it is because the constant is precisely what it is.)

Second, the billiard ball example is invalid. It doesn't matter exactly where the billiard balls are if you're getting hustled. Neurons are not typically sensitive to the precise positions of their atoms. Information processing relies on the ability to largely overlook noise.