Another geo-engineering idea is to speed up this mixing by pumping air deep down into the oceans. Personally (as a PhD geoscientist), I think that taking CO2 out of the air, compressing it to a liquid, and re-injecting it back into the geologic formations that the oil came from in the first place, is the procedure for getting rid of CO2 that is least likely to screw things up even more. It would just go back where it came from (many caveats, but basically can work).
Start raising a tax on CO2 emissions and at the same time start paying people to put it in the ground. Raise the price on both each year and you could reach equilibrium pretty fast. Should have started 20 years ago, but now is better than never. Maybe start at increasing it at $10 dollars a ton/year. $10/ton is about $4 per barrel of oil. If people saw that sequestering CO2 would pay $100 a ton in a decade the research and excitement around the ideas would be huge and likely encourage many breakthroughs. Isolated solar and wind farms extracting CO2 from the air and pumping it underground could be a huge business.
Edit: $10/ton CO2 is more like $4 a barrel than the $2 I originally wrote. Source: https://pyrolysium.org/how-much-co2-produced-by-burning-one-...