I was stationed on Kodiak for 3 years and hunted blacktail extensively. And counter to almost every other game animal I hunted, I was very successful. I notched 2 SCI minimum typical bucks. I hunted what they call the "road system" primarily.
I got one in velvet on opening day (August 1.) Early August is fairly easy to hunt because the landscape is lush green and the brown deer really stick out, making spot and stalk very straightforward but often physically difficult. The deer tend to hold high in the bowls and mountain meadows. Average daily chance of rainfall is about 30%.
By early September, two things have changed. The deer have dumped their velvet and the very prevalent cow parsnip. has died. When it dies, it turns blacktail brown. That means every dead plant stands out like the blacktail did a month earlier. That means lots of glassing. The deer will still be high, you'll just have to spend more time spotting than stalking. By the middle of September the average daily chance of rainfall is 40%. The deer slowly start moving down the mountain as the days get shorter and cooler. September can be very wet. Rain can set in for days on end. It doesn't rain hard by continental standards, but it can rain relentlessly.
By early October the vegetation on mountain tops is gone. The deer will be feeding lower. Early October can deliver a dusting of snow. By late October the higher mountain peaks will get snow that stays. The deer will be gravitating toward the beaches by this time. I never did the beach hunts.
You'll need a frame pack and game bags. You'll need to quarter deer to haul them out. Man, was that ever a surprise for this redneck. I was used to dragging them out or going to get them with the 4 wheeler. Get a GOOD waterproof topo map. You can look up the mountain and think, that it's a straight shot to the deer you see. The topo will show that impassable gorge. It will also give you clues about the best path to stalk deer. Buy very good rain gear and waterproof bags for your gear. You are screwed when you gear gets wet. It's not like the sun will come right out and dry it. Get a PLB. It can be the best $250 you ever spend.
Don't obsess over bears. The are there. They are big. But they are very good at avoiding people. As much time as I spent in the wilds of Kodiak, I only saw 2 bears up close. I saw several more along the roads, but I don't count those. Contrary to popular belief, they don't come running at the sound of a gun. At least not in my experience or the experience of many people I know and trust. If they did, come opening day of bear season, people would fire shots as a bear call. That doesn't happen.
Kodiak blacktail is the best game meat I have ever eaten. It is just incredible. They have a good layer of fat on them by the end of the summer. Cut it all off. Rope off some time to fish for silver salmon. They'll be bright and hungry and in the inland streams late October through September.
I am sorry I can't give you any details on outfitters or fly in/out services. It's been too long since I was there.