Hi All, apologies, other priorities have come up in the last few months. I wanted to chime in that I haven't forgotten about this thread, I am still slowly working on it, but it's hard going. Understandably, any locals I know or meet during this process that know anything about stag hunting try to set you up with their buddy who is a guide, who charges 3-5k. My ideal scenario currently is to find a rancher who will let me camp out (no services needed), take 1 stag, and stay for a week or two, paying $500-1500 in trespass fee. I know it's out there, but the leg work is insane on this. It needs to be a ranch that has stags, but doesn't have a hunting lodge leasing or operating on it. Additionally, it's not like every valley in Patagonia has stags, they are in certain areas and not in others. Sometimes the difference of a few miles in the same altitude, terrain, and habitat can mean lots of deer, or literally no deer. Also you need to find a ranch that has some open country on it with timber, because you cannot hunt pure timber down there, it's just too thick.
The other important thing to know is that you can't really hunt the public ground down there with two exceptions. There are lottery hunts in the national parks, but require some sort of guide service to be hired to go with you $$$. There is an interesting option I have been looking at down near Lago Fontana, Argentina, which has a good stag population and some sort of public access allotment on ranches, but it's a hard nut to crack because it's super rural, not a lot of English spoken, limited internet access, and even finding contact info for people to figure how it works is hard.
The other difficulty is regulations, it's very hard to understand if you can bring a firearm into either Chile or Argentina if you are not sponsored by an outfitter. I think the best hope is probably an archery hunt, because bow importation is not restricted. Honestly, I can't even tell from the regulations if either Argentina or Chile allow unguided hunting by foreigners! They don't have a big game brochure or anything like that laying around the internet.
Please add any info you have found out and good luck!