Seeding the “desolate zone” of the ocean with iron is probably the most cost-effective way of removing CO2 from the atmosphere…recent experiments show a fixation rate of 300,000:1 CO2-to-Fe. While I am not an expert on the latest commodity prices of iron…it seems that ~3000 tons of iron per year could feasibly be used in such a fashion pretty cheaply. So cheaply that the $25 million prize would actually be a pretty nice incentive….coupled with the carbon credits that could be exchanged for a profit. There’s at least one company who plans to make a business model out of exactly this process.
Direct sequestration via liquefaction/injection seems to be a “brute force” approach…no matter the energy source being used it will never be efficient enough to use as a global-scale solution in the time-scale that we’re interested in. Leveraging nature’s own mechanisms will nearly always yield orders of magnitude in improvements of efficiency and costs since the sun provides the energy to drive the processes. Focus fusion’s best contribution in this area probably lies in the elimination of future CO2 emissions over time as fossil fuel energy sources are phased out over the next few decades.