I agree that running the game and streaming are two of the best ways to expand the game. I also think that if the question is "how to make the game more popular," it's essential to look at currently popular games and see what they are doing. And the answer to that question might not be what existing players want to hear.
Sure, but no one has actually established that Traveller isn't one of those "currently popular games.". Mongoose is successfully selling lots of merchandise. Every time someone posts some list of "games played on some site" Traveller is one of the top space opera games. It's rules are a adamantium seller on DTRPG, in addition to the hardbacks and pdfs that Mongoose sells directly.
It's obviously not on D&D's level. Nothing is.
With the games like Star Wars and Star Trek, it's hard to winnow out the mass of IP fans from the people who actually play the games. Those games don't seem to have anywhere near the product support that Mongoose Traveller does. They "seem" to have more players in online spaces, but there's no solid figures for players or sales I'm aware of.
Starfinder is usually considered to be more popular than Traveller, though I don't think anyone has any information on sales. That's based, again, on games on online platforms.
One can always do better. But the OP's premise that the game is doing badly and needs to change things up significantly is, frankly, an unproven assertion. Maybe it is, in fact, an unpopular game. But I don't see any evidence of that. It doesn't show up on lists of janky games no one plays. It has all these new players around to tell the old guard what awful people they are.
I've never had a problem finding players. Ever. In 45+ years. Whether it's a game store, gaming convention, gaming club, online, the fact that I'm willing to run the game has been all that's necessary to get people to play it. There's no shortage of product support. There's a fair number of youtubers that talk about it regularly, though Seth's the only one you might call "Mainstream". There's a range of live plays available for it, especially by non-fantasy game standards. There are third party companies that make a living off licensed games based off the Traveller rules.
It's a game that's been around for 50 years. It's not the new hotness by a cool internet savvy indie designer to get a lot of chatter and people going "oooh, we should boost that game, it needs the exposure!". On the other hand, Traveller's going to come up (antiquated memes and all) if you investigate space sci fi games. Especially if you aren't looking specifically for horror games.
There's stuff that can be done better, both in terms of products and marketing. But I don't know where this idea that's its doing badly comes from.