Trying to figure out how does this work...

I've used Skill Trial on Sasuke to unlock Chidori Stream Y+2 and Kirin Y+1. Obviously, I can't use Skill Breakthrough on those because of the mutation. However, I was wondering if I could change those skills back to their original versions (blue Chidori Stream Y+2 goes back to basic Flame Jutsu, and green Kirin Y+1 goes back to green Kirin +1), and then use Skill Books to push the base skills to their gold version (Flame Jutsu +1 and Kirin +2), would that also unlock the mutation's gold version as well (Chidori Stream Y+2 and Kirin Y+2), or would I have to spend countless numbers of Experimental Vials and Powders to get the mutations to Gold standard manually?