Solar opacity, neutrino signals and helioseismology

In connection with the recent suggestion by Tsytovich et al. that opacity in the solar core could be overestimated, we consider the following questions: i) What would a 10% opacity reduction imply for the solar neutrino puzzle? ii) Is there any hope of solving the solar neutrino puzzle by changing opacity? iii) Is a 10% opacity reduction testable with helioseismological data?