Daydreaming here a bit, but suppose the 3 developers banded together, went to the top decision maker in the company, and proposed that they fire 8 or 9 of the managers, keeping the best 1 or 2, and that the developers' salaries be immediately doubled going forward. It could be stated or left unstated that the developers are willing to quit (which is still better than being eventually fired if the project fails, or becoming burnt out). If the project is truly important, and the situation really is 10 non-technical managers pushing 3 developers, why not try something audacious?
When people started quitting after being demoralized by repeated benefit cutbacks and layoffs, they said "We heard you, you said you want raises (after a year of no bonuses and two years of no raises), we're going to get them to you!"
With all that money you saved by laying off like 30% of the entire multinational corporation? Great! These should be decent raises! After the raises were finally granted, it wasn't even enough to cover a cost of living increase for a single year, let alone the two years that had passed with frozen salaries. And then they congratulated themselves in a corporate email sent to everyone for "listening to their employees and giving them what they ask for".
Oh, and they're still closing offices and laying people off, and expecting everyone to still keep serving paying clients (other corporations) at the same level of service they did with 5%-50% of the staff they had beforehand.
Any money they save, just stays in the corporations' hands. They don't care to give any of it to the peons. They're totally interchangeable cogs anyway, right?
The people at level n+1 to you in an organisation are there because they have the support of people at level n+2 and so on.
If you want to pull a stunt like this you need the support of someone level n+4 in a different department who hates whoever is n+3 in your own reporting line.
Which, true, means they would be better off than before.
Management are like a cult. They've all gotten to where they are because manager A has dirt on manager B, and so on. There should be no non-technical management in tech, and they should be the first to be automated.
Even if the managers like your idea and follow through with it 1) the friends of the lower-level managers take umbrage at having been bypassed;
2) the top decision maker might choose to view such bold action-takers as a threat to his/her own position.
This also goes for product suggestions, process improvement ideas, etc. People like hierarchy and don't want it (their place in it) threatened.
So, if the 3 developers are willing to band together, they should just do so to quit and form their own company.