I would definitely want to fly with Golden Eagle if you hunt out of Kotzebue, they run a good outfit there. I would assume(?) that he has already booked his caribou hunts for next year, as 40 Mile has. If he hasn't booked his hunts for next year yet, find out when he takes calls and books hunters...
No need to go guided for caribou, bou hunting all depends on where the animals are moving and if they are in the area, and that can be hard to determine as they can change their mind (and direction of travel) on a whim. Hunted the 40 Mile country this year with a friend, and we saw over 150 caribou per day, while other camps were seeing far fewer animals than we were. Back in 2015, my hunt partner and I photographed 3 really nice bulls on the day we flew in, when we could not hunt. Then the weather changed, a cold front came in, the caribou changed direction, and we saw about 100 animals total in 6 hunting days, with many being cows and calves.
If I had one shot to hunt bou, going with Jared out of Kotz, or 40 Mile out of Tok (if you could secure a spot), would be the two places I would look. There is good bou hunting in the Brooks, but there also seems to be more instances of some camps seeing lots, and some camps seeing none. And, lots of tussocks to deal with on a Brooks Range bou hunt.