Labor law makes it difficult to achieve, sadly. The NLRA only provides for bargaining units within one employer. Unless you can get an industry wide coalition to voluntarily recognize your union, it is not happening.
The path to winning such changes - whether through changing the law with the political process or simply forcing employers to bargain with industry wide strikes - requires much more powerful labor movement. The path to that is simply to build whatever power is possible. Right now the labor movement just trying to get organizing and union membership on the upswing, and I think that's the necessary step from where we are today.