EDIT: Oh, wait, I do have one more question. In order for this to be an effective form of carbon reduction, how much will the fish population increase? As the supply goes up, the prices will go down, and I'm still not convinced that the amount of carbon capture needed is economically justified by the increase in fish supply.
You could choose to run the whole operation semi-inefficiently where you chose to only catch and sell a portion of the fish, or use the fish as feed for other higher value fish like salmon and bluefin tuna.
My minor contribution to the idea was to workout that you don’t need purified phosphate to fertilise the oceans. We could just use phosphate rich rock to make a slow release pumice-like fertiliser that floats on the surface (using a photo-degradable polymer). This gets the phosphate cost down from around US$1600/t to something under $50/t. I wrote a paper on this many years ago, but I never got around to publishing it. I might try and turn it into a blog post if I get a chance.
The response to phosphate addition is surprisingly fast - depending the fish you wanted to harvest you are looking at a couple of years at most before you had a harvestable amount of fish to sell.
The law in this area is uncertain. Under the various international treaties it is not legal to dump garbage in the oceans, but no one is exactly sure where phosphate fertilisation sits. Even if turns out to be illegal all you need to do is find a friendly pacific island nation and do all the phosphate dumping in their waters and let the ocean currents do the work for you :)
The nice thing about this idea is that it turns what appears to be an impossible dream and makes it possible to make a profit solving it.