I found the Boston Metal link particularly interesting. If you consider it, combined with a small form factor nuclear reactor, you could build an iron ingot producing plant right on top of the deposits in places that would otherwise be forced to ship ore out for external processing.
They're both interesting, but the aqueous approach has some advantages. Keeping materials working at extreme temperature is difficult: basically anything above 1000C gets very hard. And a low temperature approach has the potential very big advantage of being highly dispatchable, since it would not have to be kept running to keep from freezing up. Dispatchable electrochemistry is like half a battery, just great for dealing with intermittent power sources like renewables.
The second link is interesting. I've only seen the paper on the old Norwegian pilot plant before that slide show. The Norwegians were dealing with Iron Sulfide waste from copper mining as the feed stock. Being able to directly reduce solid iron oxide is probably better.
I have also wondered if you could use the iron rich gangue from bauxite mining as a feed source.
There is a paper by a member of a Norwegian research group that ran a pilot plant in the 1950's using iron sulfide as a starting material. I think their efficiency was ~4kwh/kg. On a straight balance sheet it's not competitive against unexternalized fossil fuel based processes. It has the same problem I mentioned with hydrogen reduction. If you're using fossil fuels to create electricity to reduce iron, you can skip that generate electricity step and use the fossil fuel directly. Which is why there has been very little work in this area.
In a world where you have electricity from wind and solar with regular oversupply. And high taxes on carbon based fuels. then I think electrowinning is viable.
Fun fact, since you mentioned Norway -- in the early 1900s, Norwegian industry also used the Birkeland-Eyde process to produce nitric acid for fertilizer from atmospheric nitrogen.
The process is not energy-competitive with other processes, but since the plants in question had very cheap hydropower energy that couldn't be exported for use elsewhere, this was not a dealbreaker.
I'm thinking that energy-intensive industry in early hydropower-friendly regions could get away with using simple but inefficient processes, since the energy couldn't be used for anything better anyway. Sort of like creating a minimum viable product of an industrial process, before optimizing and getting great efficiency increases.
The paper I saw was doing it using an aqueous process at ordinary temperatures. Capital costs of the actual cells would likely be very low. Though feed stock processing might not be.
One of things that struck me is if the capital costs are low enough an aqueous process should be something you can bring online and offline rapidly depending on current market rates. Consider Germany already had a few late nights in winder where rates went negative. You can see where I'm going here.
You can't just replace natural gas with hydrogen. Biggest issue is the piping.
Here in the Netherlands we have a lot of natural gas infrastructure (it used to be mandated that every house gets a gas pipe for central heating and cooking). We would like to reuse it for hydrogen, but the pipes we have right now would leak horribly.
Beyond the issues of containing hydrogen, there is another difference. You can't (easily) liquefy hydrogen, whereas liquefied natural gas (LNG) is a big thing.
If/when hydrogen becomes cost-effective via direct market forces or mandated at gunpoint by government, the technology is ready.