So, I'm on my way back and will try to capture a little of what I learned about hunting. Like I said, the regulations and permits are pretty straight forward if you make a few calls to the game management office before you go. I hunted the archery only portion of the private side and did not participate in the state controlled hunts. There is no shortage of animals, but don't go expecting the Joe Rogan experience as he was hunting the guided only portion which I would classify as a glorified canned hunt. The other areas are full of educated deer and sheep that aren't fond of humans. I didn't hunt any of the rifle units, but if you are interested in harvesting an animal, I am quite certain a day or two would be more than adequate. If you want to go on the cheap, try your hand at the archery areas and prepare to be humbled.
You can hunt and stay on Lanai cheap if you do enough digging. I won't give specifics, that's your job, but it's easy to find info if you talk to a few people. There are reasonably priced cars and rooms if you look around and finding that info is part of the experience.
I probably wouldn't go there just to hunt, but adding a few days of hunting to a vacation is well worth it. It is an amazing island full of wonderful locals.