Sadly, the world doesn't work in the way you describe.
If innovations that would be more efficient than the current options got the funding they deserve, the world would already look very different. Like a big tree stealing most of the water and sun from surrounding sprouts, the dominant systems in society will strangle funding from its competitors. The least we can do is to help the sprouts that won't pollute the atmosphere as much by providing more funding.
Trees aren't gonna fix this.
Maybe not, but the effort described, planting trees, is not a bad effort. It's not just a carbon sink: restoring forests would also restore habitats for many of the species keeping our planet alive. Finding a solution at all that "soaks up" the carbon we've emitted so far is a pipe dream. We're already at the point where the planet has so many problems other than CO2 that we are going to have to live with the consequences for the next few hundred years. The agenda is to adapt to a lifestyle that will not make it worse.
May your grandmother rest in peace, and save her soul.
You are absolutely right that the public must be reached, and that the media sounding the alarm isn't being taken seriously. But I'm afraid that the newspapers and media can't do much else. We should be happy that the world seems to finally start to look the consequences in the eyes.
If there are any remaining doubts in your mind about what measures need to be taken, and whether those measures are truly worth taking, I highly recommend reading the foreword to "How Everything Can Collapse" by Jem Bendell. The focus of that text is sympathy, which got the message across for me. Sympathy is something we're going to need in the coming years.
Parts that positively cannot be assembled in improper order will be.