I’ve never done it out of Kotzebue but I have out of Kodiak (live up here as well). The issue is always how many folks on the plane are trying to do exactly what you are doing. If it's just a bunch of locals on the plane, you will have no issues. If however there are other hunters and they also were successful it's whoever is willing to pay the most. AK airlines cargo uses a three tier system for prioritizing air cargo. From Kodiak to Anchorage, each tier is roughly 2.5x cost. General ( as space allows), priority, and express. I paid $350 to priority my gear down to Kodiak last fall, when I returned unsuccessful and used general it was $140. Only difference in weight was the 40ish pounds of meals and wood logs we took for the camp stove.
Don't expect them to tell you honestly whether you can pay general and get it on the plane. Those folks read off a script, if it's time sensitive and must get on this plane use goldstreak express. The guys in front of me at Kodiak had gotten two Elks and were paying goldstreak, I’d bet their bill was $2K based off their pile.