Program Officer for the National Foundation for the Centers for Disease Control and Prevention (CDC Foundation)
Cochrane is an important potential ally to EA. I'm technically a Cochrane author after being part of a team that submitted a review protocol, though I haven't been closely following their work over the past couple of years. Cochrane has traditionally been strong on evidence-based medicine and treatments, i.e., drugs. They have expanded in recent years to cover other important topics as well.
The typical Cochrane review is first proposed by a team of researchers in a protocol. The protocol is considered by a Cochrane Review Group (https://www.cochranelibrary.com/about/cochrane-review-groups) and moves forward from there.
The general public may be able to participate through various crowdsourcing efforts managed by Cochrane. A quick summary of those ways to get involved is here: https://www.cochrane.org/join-cochrane
The Cochrane Handbook is a great resource on evaluating research evidence and conducting systematic reviews. It is available online: https://training.cochrane.org/handbook
Effective altruism probably has received minimal coverage in TV news because EA does not offer compelling content for TV news. EA doesn't have riveting visuals like a war zone, building fire, or local crime scene. EA won't help viewership for outlets and doesn't provide many newsworthy moments--even someone making a massive donation can only really get reported once. We often think about bias in the news media from an ideological perspective, but an even more important bias is the needs of the medium itself. TV news wants something new and interesting to show and talk about in a short, easy-to-understand story. In contrast, EA has received far more meaningful coverage in print/digital journalism and podcasts where different factors are at work.
Should we care about how much airtime EA receives? Maybe. It sounds like you're envisioning a goal of widespread awareness of effective altruism. Increased EA awareness might then influence charitable giving , motivate more people to pursue EA-related jobs, and so forth. A communication campaign could help, and that would usually start with a goal and target audience. In the for-profit world, you're often marketing a product or service to a relevant group of people to increase sales. In the altruism context, you might be trying to change knowledge, beliefs, or behaviors (e.g., get vaccinated or donate to our nonprofit).
Television is a diverse and important medium but should be seen as a tool to share information, not necessarily an end goal in itself or even a metric for success. But if you want to embrace a big goal of widespread public awareness, the Diffusion of Innovations theory pioneered by Everett Rogers is a good place to start. Effective altruism is an "innovation," and there are many strategies and tactics to diffuse or spread this idea through a group of people.