There's an enormous amount of infrastructure behind the big ones. They save up enough money to pay wages during strikes, they lobby heavily on the state and federal level, etc.
Sounds like a non-profit startup problem to build out tooling to rapidly form, run, and govern unions.
I don't know how you'd replace decades worth of strike warchest funding and long-term relationships with legislators.
You'd presumably be making a trade off for a more efficient/responsive/differently-cultured union. This may be worth it if there is otherwise a large mismatch between who the union currently serves and you. (Or a conflict of interest; are you putting out of business one of the union's large employers?)
I wonder if the unions would be friendly to a kind of affiliate relationship, and/or paying dues into a kind of program like the deposit insurance that banks pay to FDIC, but for strike insurance or something?
The affiliate thing might be interesting. Insurance is a no-go though. There would be incentive to strike to get more payout on the policy. Or worse, an insurance company would take it and would audit every strike for "legitimacy."
That's effectively what the unions are providing. Strikes are not random events, so there's no way to use actuaries to establish minimum costs for the policies though.