There are three main problems with your argument. The first is that, even taking the calculation on its own terms, you erred by three orders of magnitude
in favor of iron fertilization. The second is that your fuel use calculation, even with the calculation error corrected, would show that iron fertilization is a vastly carbon-negative use of fuel. The third is that your entire argument is based on a massive set of misconceptions.
So it's a terrible devil's advocate argument. I'd advise Old Scratch to fire you and see if he can get a public defender instead.
First, let's correct the calculation results. You've calculated that shipping 3 billion tonnes of iron powder 1000 miles from shore would burn almost 5000 tonnes of bunker fuel. But that is incorrect. It would burn almost 5 million tonnes of bunker fuel, according to your numbers:
You have: (3 billion tonnes / 80000 tonnes) (1000 miles / 12 knots) * 44 tonnes/day
You want: tonnes
* 4978509.7
/ 2.0086332e-07
That is, the calculation comes out to 4.98
million tonnes of bunker fuel, not 4.98
thousand tonnes of fuel as you said.
Second, let's tackle the implications of this calculation, if it were correct. 4.98 million tonnes of bunker fuel, taking your figure, is 4.23 million tonnes of carbon, which is 0.004 billion tonnes. Since we're stipulating that this is the cost of removing 1 billion tonnes of carbon (and a larger amount of carbon dioxide) from the atmosphere, this is 0.996 billion tonnes of carbon dioxide removed, net. Your hypothetical fleet of ships used less than 0.5% of the carbon dioxide removal budget. According to your calculation error, it would have been 0.0005%, entirely insignificant. If you're trying to advocate for Old Nick, you're doing a terrible job.
Third, let's tackle some of the underlying misconceptions behind your argument, although I have neither the time, nor the patience, nor the knowledge to refute all of them. Iron fertilization is not carried out with iron powder; it is carried out with ferrous sulfate, which is water-soluble and consequently does not sink to the bottom as you suggest.
Ferrous sulfate solution is commonly carried in tankships, which are in fact "a specific thing": https://en.wikipedia.org/wiki/Tankship. Ferrous sulfate is enormously cheaper to prepare from rock than iron is, and in particular produces enormously less carbon dioxide emissions, because it does not require reducing the iron to its metallic state, much less "grinding [iron] to a powder". In fact, in many cases, it does not require reducing the iron at all, because it's already in the ferrous state in rocks. It is industrially produced in vast quantities as an industrial byproduct of steel pickling and titanium refining (mostly for pigment production, not for the titanium metal), and, where required, by burning fool's gold. According to news reports, it's about a billion-dollar-a-year industry; it costs about US$2 per kg at the garden store, which puts a floor of 500,000 tonnes produced at present per year; however, a lot of it is currently treated as merely a slightly hazardous chemical waste.
Iron ores are mostly not, as you incorrectly assume, trucked across land, because they are sufficiently low in value that it is not profitable to do so. Instead they are transported by ship or train. But this is irrelevant, because no iron ore would be mined for iron fertilization.
However, even if iron were to be mined and reduced to obtain the iron required, this would be an insignificantly small impact. 3 million tonnes of iron per year are required to sequester a billion tonnes of carbon; current global steel production is about 1600 million tonnes, so this would be about 0.2% of current global steel production. Again, though, this is irrelevant because ferrous sulfate can be produced directly from iron pyrite without reducing it.
You assume that iron fertilization ships would be propelled by burning fossil-fuel carbon, thus adding to the atmospheric carbon dioxide burden, although the amount added is insignificant compared to the amount removed. But we're talking about a future in which serious measures are being taken to combat climate change. So it's likely that ships will be driven by Fischer-Tropsch synfuel, not fossil fuel, or, in many cases, by kites, or even by solar panels onboard. (It seems likely that the depreciation costs of ships will drive ships to continue to go fast, though, and that probably can't be done with solar panels.)
The 16 tankship trips per year we're talking about here are insignificantly small compared to the current total global shipping industry, so their total environmental impact --- aside from the iron fertilization itself --- is also insignificantly small. No purpose-built ships would be needed, and indeed the amount of shipping needed is so small that it would not justify the cost of building even a single purpose-built ship.
As for the overall environmental impact of iron fertilization, it is true that it is somewhat unknown. But some experiments have been done, and results are promising; the high-nutrient, low-chlorophyll "desolate zones" of the ocean where this would be done, amounting to 20% of the world ocean, though not entirely devoid of marine life that could be harmed, tend to become much more fertile. That is, the total ecological impact is unknown, but the balance of the evidence suggests that it's positive. The impact of the iron on ice formation is of course nil because the quantities of iron we're talking about are tiny traces; although presumably algal growth could affect ice formation, it would promote ice formation, because algae strongly reflect infrared light, while desolate waters are almost perfect radiation absorbers (albedo around 10-20%). The larger concern is that there isn't enough ocean that could be fertilized to absorb more than a fraction of atmospheric carbon. I suggest that you read https://en.wikipedia.org/wiki/Iron_fertilization and https://en.wikipedia.org/wiki/HNLC before commenting further.
In short, you have not done your homework and appear to be merely making up random arguments with no basis in reality. I regret the need to state this so bluntly, but my previous polite and encouraging comment on the subject has been both downvoted and flagged into oblivion.