From the linked article: The idea for a ship made of ice impressed the United States and Canada enough that a 60-foot (18 m)-long, 1,000-ton ship was built in one month on Patricia Lake in the Canadian Rockies.
Not joking. I like the dream big, what can I say :)
More specifically, imagine ships sailing around the Arctic circle just before the water freezes in winter, dropping sawdust (or newspaper for "super Pykrete") in their wake.
Since sawdust comes from trees, it's sequestered carbon. Once you put it in the water, it's not going to burn down and release its carbon like a tree in Australia or California might.
Since it floats, it should stay near the top of the water until the water freezes. Pack ice with sawdust frozen in it will last longer and reflect the sun's light back for a longer period of the year. There's a risk of the albedo being affected negatively--perhaps using light-colored wood for the sawdust would help with this.
Hopefully, even after the Pykrete melted, the sawdust would stay in the ocean near the surface, and re-freeze next year so you get Pykrete every year. (A potential downside here is that the sawdust could be difficult to remove if we ever realized this plan was backfiring somehow. Maybe we'd prefer some sort of sawdust which eventually sinks for that reason.)
Another idea is to bioengineer some kind of organism which reproduces in the Arctic ocean and changes the consistency of the water so that when it freezes it behaves more like Pykrete. Perhaps some kind of algal bloom (apparently you can trigger algal blooms by seeding water with iron?) To be safe, before releasing this organism into the environment, we could bioengineer some other organism which feeds on this and nothing else, so we have a way to reverse the experiment if it goes wrong.
Hey, I don't think it is much more harebrained than other geoengineering ideas I have seen floated :)
This reminded me about Kovrigin's chronicles, a story by Vadim Shefner that I read as a kid. It's somewhat musing on the soviet research atmosphere and all, but the background there was that a man invented a way to turn water into a special sort of ice which could be used as a universal unbreakable material, with a bold idea of building cities under the ocean because there is so much space on our planet.
This is very interesting and imaginative work from a great group but the headline is not justified by the story yet.