I think the fundamental mechanism for addressing the question of how to increase representation of currently under-represented groups is encouraging multi-member nominations from individual parties. That is clearly what has worked in many countries.
On the particular question of how many women are elected under different voting systems, I think STV gets a bad rap, because it is used nationally only in two countries, Ireland and Malta, and both of those have some very significant societal issues around the representation of women. Even so, Ireland's European parliamentary delegation is 55% women elected under STV.
In Western Australia, in 2010 to 2013, the upper house was 47% women at a time when the lower house, the council, was 22%. Their senate is 41% women, 26% in the lower house. This is all because of STV. It's a complete myth that STV is not favourable to the election of women.
In Canada, the political scientists tell us that Canadians have no gender preference in whom they vote for. They will vote for the most qualified person put before them. Where the limitation has been is in the nominations.