Husky,
I lived on Kodiak for two summers and hunted deer there extensively. While my experience is limited to late summer/early fall while the bucks are in the alpine and reaching them is a chore, I've always wanted to go back and hunt them with a bow during the rut in November... maybe do a sea-duck hunt as well.
Living on the island in the bush afforded me ample opportunity to spend time around bears, escpecially a specific set of them. I never had issues with them but did have one come in to about fifteen yards downwind as I was boning out a buck. I stood up and began shouting and the youngster realized what I was and lit out for the berry patch. I carried the Alaskan Swiss Army knife of calibers; the .338 Win. Mag. and it served me very well on Sitkas. You are correct in your size estimate but they are more short and stocky than small. In my experience they were as heavy or heavier than most whitetails I've killed and they are tough to boot. I never knocked one off its feet with the .338 despite breaking shoulders on several different bucks. They always seemed to make it to the brush which added to the excitement, not knowing if the man in the brown suit was taking a nap in there.
If I were doing a DIY I would look at the many forest service cabins scattered around the island with the area around Karluk Lake or Frazer Lake getting my knod. There are several air services in Kodiak that would fly you in and pick you up. The ones that come to mind are Island Air and Andrews Air.
Take good rain gear, good boots, fly rod, and good camera equipment. I would also recommend packing a shotgun as well as your rifle. As for a rifle? It is difficult to beat the various .300's or .338's up there. Much bigger is a joke and much smaller and one runs the very real risk of not bringing enough gun for a possible bear fight. If I were doing it all again I would carry a handgun in .44 mag or larger, something compact and unobtrusive, and take my .257 Weatherby for the deer hunting.
In short, this is an awesome hunt that can be very physically demanding and potentially life threatening (read affirming), Alaska has many ways to test a man.