As a scientist, the first thing I would ask is what the question is directed at. Is the presumption here that they are a predator of salmon? My first step in that regard would be to establish that that was the case. Before I would say we should go out and increase the harvest of striped bass, I would want to be sure that the problem existed.
So that means a comprehensive study first or at least a census by people who are already angling them. In fact you don't even have to spend a lot of money; there's already an angling fishery out there for them. Assess those fish that are captured and taken home to see, over the course of the period that striped bass are out in an estuary, what they are feeding on.