If you aren’t familiar with case studies like sickle-cell anemia, lactase persistence in humans, sexual selection in peafowl plumage, etc., you should probably read a good textbook on evolution before doing any more speculating.
“Pulling some hormonal levers” is highly non-trivial. Think about what sort of genotypic change is needed to affect the relevant hormones at the right age, in the right tissue, without side-effects. Read up on Accutane (isotretinoin) to get an idea of what else can happen when you try to get rid of “zits”.
Also, what gives you the idea that we are anywhere close to any sort of genotypic equilibrium?
The description of the coin flips having a Binomial(n=?,p) distribution, instead of a Bernoulli(p) distribution, might be a cause of the mis-reading.