What part of Kodiac are you going to ?
I went there in 1996 for a sitka
black tail hunt and stayed in the saltery lake area. there are only 3 species of big game on the island the goats, the deer and the bears and they are all there in abundance. I went in sept. so I dont know if the bears will still be out in november. just for a bit of advice make sure you get in good shape the vegetation is so thick that it saps your energy hiking through it (of course the goats are above the vegetation but you will still have to go through it to get to the top)whatever you are planning for film or chip space on your camera at least double it, this place is the MOST beautiful spot on the planet (that I have been to anyway) and yes a 338 Lapua will be perfect. I used a 7-30 waters pistol to shoot my deer and freely admit I WAS A DUMB ASS to do so.
I guarantee you will have the time of your life as long as you are in good shape. B