If I were the players, and considering what our "ask" should be, I might prioritize trying to have the NBA lean on the networks that broadcast their games and have sister news networks (TNT -> CNN, ESPN -> ABC), to alter their coverage of the social-justice movement.
Tactically, that might include things like more explicitly labeling provable lies by politicians, specific close-up coverage of local policing, greater emphasis on sharing news and best practices around policing and justice policy, and a willingness to allow, even encourage, anchors to voice their own opinions to call for change or action (e.g. to call for holding specific people accountable). There are doubtless many other ways that they could find ways to improve the honesty, thoroughness and relative emphasis of the topic on general news coverage.
This isn't the days of the Big 3 Networks, but ABC and CNN still have a tremendous amount of power to shape opinion. It's not quite what NFL and MLB players could do to lean on Fox Sports and the regional affiliates, in terms of reaching incremental people who need to hear the message, but it'd be a big start and could result in some snowballing in that direction. And IIRC Fox does a lot of MLS coverage, so that might be an even likelier vector for the calls to spread. It'd be a bold but achievable goal.