Every time I read something like this, my hubris alarm goes off. We couldn't even get trans-fats right, so I don't see how we're going to cover all the contingencies for something like this.
'Terraforming' earth has never been easy but it has long been necessary to feed humans. Bulk addition of soluble/leachable nutrients (naturally depleted by rainfall, fractionation by gravity, and chemical transformation) is the primary novel intervention in modern agriculture. We've learned that biological systems can be made to cycle much faster by turning the crank in this way. The rewards are great-- used in land, 7 billion fed. Use of similar intervention in the ocean suggests proportionally larger rewards.
Further, we've already destabilized the global system by injecting carbon. It is now our responsibility to find a way to stabilize it again.
Whether the unknowns will get us is.. unknown. We are going to learn about whole-planet ecology in the next century whether we intervene or not. Pretending that we know less than we really do is kind of a trademark regressive-right tactic, so you'll forgive me when I say it's quite disengenuous and harmful to compare coal combustion to iron fertilization.
The negative externalities of coal combustion have been known in broad strokes at both the macro and micro levels for centuries. The benefits of fertilization have been known for much longer.
We thought saving the Ozone Layer by switching from CFCs to HFCs was a good idea.
Joke's on us! The HFCs currently in use in systems worldwide, if vented and not carefully incinerated, will trap as much heat as all the CO2 in the atmosphere, for centuries.
Specify propane or ammonia systems, and make sure existing systems have their fluid extracted professionally.
At some point you have to choose what to do, and that's always going to involve unknowns. For instance: 40 years ago, the USA could have chosen to continue building out nuclear power. Not accelerate the deployment, mind you, merely continue the roll out apace. If we had done so, we would be completely free of coal and gas today. Not maybe 30 years from now if we hustle, today. One could rage all day against the risks of another meltdown that this would entail, but when one considers that the "reasonable cool-headed alternative" we chose instead was to pump the atmosphere full of CO2, suddenly that doesn't seem too bad.
It's easy to rant about the negatives of any given tradeoff, but for the rant to be meaningful, it has to be compared to the alternatives, which in this case are "do nothing, adapt to climate change" and "spend truly mind-boggling sums of money to accelerate renewable rollout." Neither of those is good. I'd personally prefer to spend the money, but I don't get to make this choice, and since "do nothing, wait and adapt" seems to be the default alternative, and it's chock-full of unknowns, it's hard for me to say that the geoengineers are significantly worse, even though their risk profile is, as you point out, steep.
Potentially destroying the ocean vs spending money to reduce carbon emissions is a no brainer, and it's the job of these scientists to say that out loudly rather than to push for these extreme solution which can produce a blackswan disaster of epic proportions that even money won't be able to save.
The arrogance of scientists to "try out my method instead" is at fault since if these scientists were to actually want to save the planet they would push on politicians to spend money rather to try and implement potentialy extremely destructive solutions.
In short, you fail to understand that this might create a unfixable disaster, while global warming is obviously solvable by other means since we are far from any kind of an serious crisis, regardless of what "scientists" say.
The world is NOT burning yet, which means we can and HAVE TO avoid stupid solutions like dumping iron in the ocean while there are harmless solutions available.
Scientists have been pushing on politicians to lower emissions at least since the early nineties. There is no discernible dent in the rise of CO2 levels. There is not even a big dent in the rise of emissions: Not even the second derivative is pointing in the right direction.