As much as I like hemp, this seems implausible. Trees sequester carbon for longer (as wood). If I was looking for a quicker alternative I'd plant bamboo (which also 'grows like a weed').
I suspect the best way is algae, but we'd likely destroy the oceans overusing it given humanity's inability to do things in a metered and sensible way.
Why set it lose in the ocean when you could contain it and measure it in a more controlled environment?
It's not immediately clear to me that the energy involved in creating a "more controlled environment" would make the investment a net positive.
In a contained setting it still will sequester carbon. It is more easily monitored for expected behavior. It minimizes risk to other ecosystems.
Algae are interesting, but I don't see them as being ideal for tying up the carbon for long - we'd need to compress it into bricks and bury them, perhaps?
Aren't we already growing algae in the ocean about as fast as we can? Is there more we could be doing than manufacturing fertilizer on a geological scale and letting a lot of it end up washing out to sea? (Honest question, I haven't thought about this avenue of geoengineering before)
Well, you'd just have to find a way to store ("sequester") the plants for a few decades at least after their initial growth spurt, and you have a good carbon solution there.
Furniture? Wood products? We already do a lot of that.
Just put them in a big pile/hole somewhere.
It should also be mentioned that the quickest and cheapest way to sequester carbon is not burning most forms of it in the first place.
I think most people would agree that "stop burning fossil fuels" is a utopian idea that doesn't actually work in practice. You're not going to get people to give up on it (at least near term) so you need to focus on solution that can actually be achieved.
In the American West at least, trees go up in flames every few years. Turning hemp into products people don't burn might be a better way to sequester carbon.