Gary gave you solid info. Lots of logistics to consider, the biggest is how to get the meat from the bush to your home. Check with Alaska Air on their antler policy, it seems to change occasionally. I think you have to cover points and wrap in plastic now? I would do as Gary mentioned and split the skull, stack them and stuff them in a bag or wrap them up.
I would budget at least a full day on the return to chase down shipping supplies. I bring it back on the plane with me vs shipping/cargo. Baggage fees are far cheaper than over-nighting stuff. A caribou will net you maybe 150lbs of boned out meat. I'd put it in a cooler, inside a plastic bag, and tape it all up. Check airline regs on what they allow for meat. I would also chase down freezer space to use the day before departure. Some hotels have space to store entire coolers/fish boxes.
I haven't flown out of Bettles (or Coldfoot), but have looked into in the past. Seems the going rate is $2500-3500pp. This is variable on who, and what type of aircraft, which also dictates how much gear you can fly. I would say you could expect to haul maybe 100-300lbs pp. But again highly variable on aircraft and number of people.
You need to decide on a transporter and call them to discuss details. There may well only be one transporter who will fly you where you are wanting to go.
Get an Alaska Airline CC, you will save on baggage costs, and may even get enough miles to fly up for free, not to mention one of your buddies can fly for "free" with purchase of another. In other words... if there are three of you, purchase one ticket, pay $125 ($25+annual fee) for the companion fair, and book the third on miles... The three of you could fly up for basically the cost of one ticket.
