I'm not sure if I'll have time for further optimization, but this is definitely min primary. This metric took me a bit longer to parse out than the first one, but I eventually decided to graph the period against the score, and I notice a quadratic relationship. After panning over possible periods for a few more solutions and doing some regressions in desmos, I found that the quadratic was in terms of rate, not period, but instead of immediately noticing that 2.28571 was about 16/7, I instead epsiloned a solution to a score of 0.001 before checking whether the arbitrary number I found was close to an actual good ratio, but I figured it out soon enough.

for the sake of completeness, I can say that metric one is *precisely*
100 * (rate - 16/7)^2 
(with default restrictions as well I assume)