At least on the part about the Nootka lupine (Lupinus nootkatensis), seems they're edible in seed and root form [1][2][3] as long as they're leeched properly beforehand to get rid of bitter (possibly toxic) alkaloids. Grizzly bears apparently also relish the roots. Some butterflies feed off the lupine. Medicinally, with less references, used for digestive disorders, skin conditions, and infections.[4]
Can probably just farm them, or harvest the fields that exist, and then store the seeds / roots or make flour out of them. Seems like a possible farm crop personally. Go out with a harvester designed for beans / peas. There's not that much that grows in Iceland anyways.
[1] USDA, https://plants.usda.gov/DocumentLibrary/plantguide/pdf/pg_lu...
[2] Sierra Club, https://sierraclub.bc.ca/ecomap/nootka-lupine/
[3] Plants for a Future, https://pfaf.org/user/Plant.aspx?LatinName=Lupinus+nootkaten...
[4] Wild Flower Web, http://www.wildflowerweb.co.uk/plant/2579/nootka-lupin#:~:te...
Annual lupin (L. angustifolius and L. albus) have been bred for better yields and low alkaloids. There are some existing commercial varieties. Australia is a large producer.
From an economic perspective, the yields on perennial lupin are just too low. Something that plant breeding could hopefully address long term.
Apparently the Land Institute already investigated it (https://landinstitute.org/our-work/perennial-crops/legumes/) and decided on sainfoin instead of lupin. I reached out some time back to ask why, because I was curious if their research found yield or alkaloid content too difficult to control for. Never got a reply.
In terms of commercial farming, it's probably desirable to have the better varieties. Maybe get some of those seeds from Australia then for Iceland. Have variety.
Mostly just a suggestion for the issue of "lots of a plants, that we don't especially want." At least it's edible. According to a quick search, it cost apparently $30 to $40 dollars per acre to harvest an existing field (Purdue custom rates survey for combines, obviously no input costs considered, Iceland's maybe different).[1] Maybe add a bit further for cutting, raking, windrowing, and threshing parts.
Either way, with an existing field you just want to get rid of, hiring a combine and running it over the field is not that expensive (based on the available prices). Throw it all in a pond, pool, or barrel and let it soak until they're safe to eat. Not horribly expensive.
On the sainfoin thing, probably just easier and less work for their objectives. WP says sainfoin's already "highly nutritious plants" used for a long time for forage and nectar production.
Frankly, they seem like a trade-off personally, since Lupin varieties grow rapidly in horrible climates and terrain. Sainfoin is apparently finicky. "difficult to establish as pasture, not persistent in grassland, do not recover well from overgrazing." Lupin is probably a better choice for anything in the artic, sub-arctic, tundra, and taiga biomes (which is most of Iceland).
[1] https://www.farmprogress.com/harvest/custom-harvesting-could...