How do scaling of the coefficients for the poles of a biquad filter affect the gain?
Sorry, that doesn't work. You have to scale all numerator (the "b") or all denominator coefficients (the "a") at the same time. That doesn't work for the denominator since you all practical implementations require $a_0=1$. Scaling $a_1$ and $a_2$ without scaling $a_1$ will move the poles and change the overall shape of the transfer function and not just the gain.