"Last September, three out of 96 employees in Engineering and Operations at Etsy were women, and none of them were managers"
How many of the 96 employees were black, and how many of the employees were black women? Should we be concerned if it was lower than the stats about women in general? If not, why?
You talk about "gender balance" as if somehow there's an argument there that is more valid than "race balance."
In terms of engaging specifically females into more tech subjects, i'll relate something i've seen here in DC. I work with Knowledge Commons DC which offers lots of free classes, some of which are tech related (Object Oriented Programming with Java, for example). That class was 75% women last time. Why? One reason might be that most of the volunteers/organizers are women, and their social circles reach out to even larger groups of women. As people seek out similar people it may make it easier for them to gravitate to subjects which might normally be perceived as male-dominated or otherwise not as open for women. Just a thought.