It would be interesting to know the acreage of the island and how many people/acre the two groups amounted to. I am guessing that the reason some islands are uninhabited is either lack of fresh water or because there's barely enough food for two adults, let alone raising a family.
If there were two teams of six on one small island, no wonder they ended up malnourished, between them. You would have thought they would have done their calculations at the early planning stage.
Even with crops and livestock, your maximum population density could never be better than early Victorian-era rural communities ie before modern fertilisers and mechanisation. I am willing to bet that 'survivalist' types under-estimate what modern farmers are achieving and how far short their efforts would fall, in an authentic post-apocalypse scenario. If they put as much energy into fostering peaceful international relations as they currently put into food hoarding, we would have a better world. But they like their guns too much, I fear. Their most important farming implement, in a manner of speaking. ;-)