I think you could potentially run an initiative process to obtain this result. It might have some unintended consequences and possibly some legal issues.

Unintended consequences could include loss of state and federal financial support for hatcheries.

Legal issues might include whether the state can do this for waters under federal jurisdiction. I don't know the law in this area, but in other areas I believe that Uniform Commercial Commerce Code limits where states can regulate, when it impacts interstate commerce. I'll bet fishing in the Columbia and the salt would run into that issue.

Finally, I doubt you could legislate away the tribes' right to fish salmon. That's an obligation on the US, not the state of Washington. So you might end up simply changing the ethnicity of those running the gillnets. You could then end up growing hatchery salmon for fishermen who pay no taxes at all on the salmon.

I'd love to be proved wrong.