Interestingly, you hint at, but don’t really acknowledge one of the classic solutions (typically pushed by the libertarians): privatize the commons. This is equivalent to your intuition of trying to set N=1.
Of course, the other classic solution is regulation, which is not too far from your union example.
Of course, both the classic solutions have downsides. Privatization makes it harder for everyone to share the good, and also leads over time to stratification and unequal society. Regulation means bureaucracy, which easily becomes captive to politics and money.