When a gut hooked fluke comes aboard we remove the hook and release it. I don't know the mortality rate and I don't know if one way of removing the hook is better than another but what we do is this:
hold the fluke so the dark side is facing you. Open the gills, find the leader, reach in, grab the leader, pull the leader to you. That will turn the hook and bring the hook toward you. Pop the hook up, thus releasing the hook from the fish. Thread the hook/leader up and out the mouth. For some reason this only works when doing it from the dark side of the fish.
I know, you should stay clear of the gills, etc, etc. But, I don't think this is any more harmful than any other way of releasing the fish. They all seem to be disastrous to me. When released this way, they always to swim away fine. Who knows how they are a day or so later.