A friend of mine was guiding goats for Alaska Cross Country Guiding out of Haines until deep into November. I think they even do the occasional December hunt. It's all extremely steep and rugged country, but it's also close to town if that's what you mean by "accessible".
Not to seem too much like an advertisement, but I also offer fully-guided mountain goat hunts until the first of December. Anyway, you asked, so I thought I'd throw that out there.