I can't speak to the Canadian situation, but I do have three suggestions.
One, I think you should articulate goals for gender equity in specific programs, and then you should audit them.
Second, for grants that the federal government gives out to provincial governments, local governments, or NGOs, I would require that when they report, they report on whether or not they've achieved gender equity goals.
The third suggestion I would have is to train the analysts in how to do this. Ideally, they'd create a cadre of analysts who would then turn around and train others within the agencies so they would know how to do it. If they don't know how to do it, then it's hard for them to comply.