The National Park Service and shown that they have no intentions to try to transplant any animal out of the parks. They showed this when the decided to cull the bison herd in the Grand Canyon. That along with not allowing hunting inside of a National Park they don't have much other choices to use to control the moose population This park is a island and is far enough away from the mainland that it is highly doubtful that any of the wolves would be able to swim to it.
It would be nice if they would allow some hunters onto the island to take some of the moose but with the type of regulations that they placed on the bison hunt in the Grand Canyon I doubt that they would get very many talkers. The last I heard anything on that was clear back in the fall of 2017, perhaps they didn't have any takers. With the hunters not allowed to keep all of the meat would be a big reason not to even apply to hunt them.
Hunting in national parks is allowed in some cases, depending on how the park was established. For example: Teton Park in Wyoming, and Voyageur's N.P. in Minnesota. I live not too far from Isle Royale N.P., and have hiked, camped, and canoed over 40 days on the island, and am planning another canoe trip there this coming summer. Few folks canoe on the inland lakes with most fishing in Lake Superior, or hiking the island. We almost always see moose when we are there, but even when there were over 20 wolves, they were never seen.
The island originally had no moose, deer, bear, or wolves, but did have woodland caribou. The caribou were wiped out after settlement in the late 1800's. The first moose appeared on the island in the 1920's (swam or crossed on an ice bridge from MN or Ontario - 22 miles). The population took off, and went through a couple boom/crash cycles before wolves crossed on the ice in the 1940's. An equilibrium was eventually established, but the generational inbreeding among the wolves led to their demise.
The predator/prey relationship has been extensively studied on Isle Royale because it was "uniquely uninfluenced by the hand of man." Oops, I guess that they didn't like natures way. The ice bridge doesn't happen every year, but did so in 2015, and one wolf left the island and was shot on the reservation. The ice bridge is back this year, and one of the first four wolves (previous to these Canadian wolves) that were transplanted has already left. They don't say so on the story, but I believe that the Canadian wolves were removed from either the Slate Islands or Michupitchen Island because they had completely eliminated the caribou and were now starving. It's curious to note that though moose are in severe decline in MN, MI, and southern Ontario, the moose on IR are overpopulating. Years of study primarily blame "climate change", but the IR habitat and weather is no different that those other nearby areas. Two factors that the IR moose don't have to deal with are deer and too many wolves.
The loss of caribou from the Lake Superior region has been ongoing for more than a century. Scattered bands hung on in northern Minnesota until the 1940s. In the early 1980s, up to a dozen caribou wintered near the North Shore community of Hovland, then disappeared. On Isle Royale, native caribou were extirpated in the 1920s. Local anecdotes and genetic research suggests moose were introduced to the island as a replacement species. When moose began to overpopulate the island, a mostly unsuccessful introduction of wolves was attempted to control their numbers. Wolves are thought to have crossed on the ice to the island a few years later.