The warnings have been sounded. The board meets. Management speaks. And nothing of substance is done. Some board members retreat to coffee shops or bars to bemoan the inaction. Among them, no doubt, are some who will seek to water down or defeat any attempts at action once they are made.
Shelley Berman once had a great comedy routine about an airline passenger who, after seeing flames shooting out of a wing engine, remains silent because he'd rather die than make an ass out of himself.
So the board keeps its cool.
There are people who would rather be cool losers than unsophisticated winners. That's why anyone who raises an alarm in a business meeting has to do so in a relatively calm fashion: "These are the facts. Here is the history. This is the likely result."
You'll be up against powerful myths, so your strategy must resemble a funnel through which the facts and logic will lead to one inescapable conclusion. You can overstate nothing because the other side will be looking for anything that smacks of alarmism or a vendetta. They will be eager to claim that emotion fuels your arguments so you must, if anything, resemble an amiable and even boring accountant but most importantly, a relentless accountant.
This does not mean that you need be on the defensive; indeed, don't be the only person doing the explaining, but avoid rudeness and accusations. [Remember "relentless."] Be wary of distractions and the temptation to strike in areas that do not matter. Find their weakest points and then gently demonstrate how those are in dire need of change.
If this is done well, no one need be embarrassed, although some may choose to be, and the focus can shift to the next stage. A group win is better than an individual win. And that fits in with your goal: To be quietly effective.