i think it has to start with having engineering managers and directors who are deeply technical themselves. the idea that you can split up this work into "managers do the people stuff" and "engineers do the technical stuff" is bananas. it's all sociotechnical work.
this is why i advocate the engineer/manager pendulum so strongly. we get better results when management has strong tech skills (and staff+ engineers have organizational skills as well).
the exception was places where leadership already thought in the same terms about software quality/etc, which meant I didn't have to do much convincing :P
how would you build teams or structures to support that sort of holistic thinking about software?