Since it's game programmers, why not apply some game theory?

Aside from not wanting to be part of a union, people are reluctant to join a union if others do not do the same. Many people might actually join one if there was a big one, but a big one can't grow because nobody wants to be the first guy to raise his hand.

So someone needs to make a website that manages this. Everyone pays a deposit, say $100 bucks, and signs onto some secure site that will keep details private. If you get more than some minimum, the money is sent to the new union. Otherwise send it back.