Went on a moose and caribou hunt this past fall, so I also researched this a fair amount. Flew out of Fairbanks, all flights/connections by Alaska Airlines to home. I know that different airlines can handle these issues differently and AA isn't always an option depending on your home airport.
Regarding the known shipper number, if you're using a planning/guided service, they will probably provide you with theirs if you ask (ours did). Or, if you use a local taxidermist in AK (we rented freezer space from one), they may also offer this to you (ours did). I wouldn't go through the hassle or especially the expense to get a known shipper number if you can just use one from one of the services you're already using (guide, taxidermist, etc.).
When I looked into using Alaska Airlines for checked bags versus air cargo, they calculate the cost a little differently, but were really close in total cost, as others have mentioned. I believe air cargo was slightly more. Personally, since air cargo had to be dropped at a different location and the cost was close (if not more expensive), I didn't see the point in using AA air cargo. I checked a ridiculous number of checked items and everything was accepted and arrived smoothly.
I had also heard about antler restrictions on AA flights, and being on a first-come first-served basis. I was also nervous when standing in line to check in for my flight and saw 4 caribou racks in line in front of me. But, when I got to the counter, everything checked without any difficulties. No issue with multiple racks on the same flight (I saw the same hunters on the plane with me, and my antlers, checked after theirs, arrived without delay).
I had caribou antlers, and had the taxidermist split them because I heard that you had to do this for AA to take them. That was also part of the pitch for using Alaska Trophy Express (which we didn't use), because using this service avoids having to split your antlers like the airline supposedly requires. But, standing in line, I quickly noticed that the 4 caribou racks in front of me were not split, since they were all well-wrapped European mounts. After checking mine, I asked if there would have been any issue if I had brought un-split antlers like those others, and the AA representative just acknowledged that split antlers like mine take up a little less space, but all antlers are ultimately accepted. In the pictures above, I'm also noticing unsplit moose antlers that flew home. After that experience, I'm left wondering why anyone would split their antlers.
Also keep in mind that your first 2 checked bags have to be under 50 lbs. and under 62" linear to avoid an extra weight/size fee on those 2 bags, but the third checked bag and beyond are all $100 each, regardless of size and weight (up to 100 lbs. and up to 115" linear). So, don't worry about keeping those additional meat boxes, luggage, etc. all under 50 lbs. each and small in size, even though they're checked bags, or it will cost you a lot more in shipping at $100 each for those. It's costing you $100 each anyway (bag 3 and beyond), so load those containers up to just under 100 lbs., and 115" linear is really huge.