Sure.
One thing I would suggest is that you do some pilot projects. In many ways what you're considering is an innovation, and as with any innovation the question is how you innovate. How do you do it?
We know from other policy examples of innovation what tends to work. I would suggest a pilot project with a specific agency or department perhaps, to see how it goes, what you learn, and the concerns and how to address them.
Second, I would think about some incentives for doing so. I think most line administrators in government get frustrated when they're asked to do something additionally and there's no incentive to do so. I think if they see it as part of their development and as some innovative thing they can be involved in, that makes it attractive for them professionally.
As I mentioned at the very outset, you need the buy-in of civil society but also government. I think the groups that would be using this analysis are the ones that need to be consulted. Again, for it to be part of the fabric of the budget, it needs to be used, and for it to be used, the potential future users need to have their concerns addressed. What is the information they would want, and how do they want it presented? I would work with them on that.