Couple things. Zach owns Tok Air, not 40-Mile air. I doubt 40-Mile has any slots open anyway for this year, but you never know. They are one of the best outfits in the state.
The feral Reindeer populations on Kodiak have been hovering around 350 head for the last 10 years or so. Hunting pressure has been increasing over the last few years like 2-3x as many hunters, and accessibility to them is limited. Not saying you can't get one, but your odds of seeing other hunters is quite high compared to 40-Mile area, or south side of the Brooks.
Prior to 2012 the harvest on Kodiak was about 15 caribou. I haven't seen 2016 yet stats yet, but 2015 was 40, and 2014 was 36. Mature bulls make up about 15% of a healthy heard. I would for sure talk to the bio before booking a trip and finding out that a "big" bull is a 3yo, much like what Adak has turned into. Unless you are just after any caribou, then I'd go to Adak and be miserable and fill up a truck with caribou.
Check with Wrights Air out of Fairbanks. Tough to find a flight this late in the game. Keep calling though.
Another option, not cheap, is the Western Alaska Range. Check with Willow Air, or transporters out of McGrath.
Cheap and easy caribou hunts are a thing of the past, and only getting worse, especially for a non-resident.
I can't wait to shoot one or two this fall.