I've found that it's enough to just widely circulate it. As you point out, it's important to have some guarantee, so that the writing seems worth it.

If it is really a good idea, it will attract the attention of other serious people and become common knowledge in the organization. The shift in common knowledge is the most important change because the problem goes from something that many think they have to live with, to something that has a solution. At that point it becomes something to prioritize against everything else.

This does present some risk to leaders, it's much easier to seem incompetent when there are solutions available that are not being put to use. Leaders need to specifically address why known solutions aren't being implemented yet, and rationalize the decision.