There are very nice trophys of both species on Lanai. The people to contact would be Palawai Outfitters. I believe they are on the web but I am not sure of the prices for either of the animals you mentioned. There was a video on myoutdoortv with someone hunting on Lanai for Mouflon. I will try to find it and tell you the name of it so you can see it for yourself.
You could also try the island of Maui, they have some very nice trophy animals there. Get in touch with Jeff from Arrow One Ranch, owner/operator. He's a friend of ours & is an awesome guide. My husband hunts there every chance he gets! Hope you have a great vacation where ever you go!
When hunting whitetails there are many different languages being spoken afield that I key on when outdoors. All these little creatures living around whitetails have something to tell us if we are willing to listen.
My favorite tattletales of the outdoors are a handful of little birds that live in my state of Ohio. Maybe yours too. A tip for the upcoming season.
There are Blue Jays, Cardinals, Chickadees, Killdeer, and Sparrows that all have language...