@Rice I feel like they could just keep digging until they hit magma and then reroute the lava to the surface to grow their island and also keep the mines from flooding in with lava so they can continue making lateral mine shafts below the ocean. At which point they will have both an underground kingdom and a growing volcanic island, like Hawaii. Also, they have all the resources of the sea and growing amounts of farm land, so I don't see the problem of limited resources. It would be one thing if they couldn't harvest the oceans bounty or if there were no fresh water on the island, but both are available. Also, there are all the magic cheats they have.
Also, if I remember correctly, the Inuit people of the arctic circle could get all their nutrition from a over 90% meat based diet. Although they did need to get nutrition from eating organ meats, drinking seal blood, whale blubber and fish eyes.