Discovery channel just showed a special in which one of my ideas was tried in a different form, and good news, it worked.
In my idea, boats would haul nutrient rich water to nutrient poor sections of the ocean, setting it into bloom and sucking enormous amounts of carbon dioxide out of the atmosphere.
In their version, they found that the deep ocean was already nutrient rich, came up with a pump that would, by wave-action alone, pump the deep water up to the surface, tested the bloom hypothesis, which checked out, and launched two pumps about 60 miles north of Hawaii.
It turns out that my hypothesis that you can feed the ocean is correct. Two weeks after launching the pumps, there was an explosion of fish in the area, plenty of phytoplankton, and loads and loads of seabirds. Unfortunately, one of the pumps was damaged by the ocean, and the show did not describe how expensive they were to build.
If this is all true, then it might be possible to convince a fishing group or government to pay for many pumps, sucking our excess carbon dioxide into the form of fish and birds. If people eat the fish, they might release the carbon contained in them, sure, but those people were planning to eat anyway. What they don't eat in fish, they'll eat in emergency rations distributed by charities.
This also helps because the complete collapse of most major fishing species is predicted within 10 years. Why are they in trouble? We humans keep eating them, as many cultures love eating fish. A tragedy of the commons occurs because every fisher wants more fish, but every fisher means less fish in the ocean to be had. The fish most commonly harvested won't go extinct, exactly, but it won't be profitable to go send a boat to get them because they will be so rare, the fisher will lose his or her boat, and life would suck for everyone generally.
Funding is the rub. That and a temporary mortorium on fishing, which would benefit everyone, especially the fishers.