I have been up there 3 times for a few weeks in early Sept. between 1994 and 2000 (drove up another time in the mid 80's). Flying with firearms wasn't too big of a hassle, but I don't know what has changed. Was pack ammo in a separate check bag, and gun case should lock. Sometimes the gate agents wanted it opened to check, sometimes they'd just ask.
The later 3 trips, I went in the area around Tok (about 80 square mile radius from there), would fly into anchorage, rent a car and drive to a place that had really competent pilots to fly the rest of the way in. Really pretty just driving around up there. I had a 7mm-08, I took 145 grain hot cores to hunt caribou/wolves with, they worked fine. I used mag primers for the loads with the idea that when it was cold, they'd provide better ignition. One year it was never below 50F during the day, another year there was 3 feet of snow on the ground and I was stuck on the side of a mountain for two weeks beyond the week I'd intended to stay, eating moose breaded in malt-o-meal and kool aid.
Never shoot a moose down in a valley. We spent a week cutting frozen solid meat off of it and hauling it back up to the top through the snow. The other two years fell somewhere in the middle. The 3 feet of snow was a freak year during an el nino though.
I also carried some 160 hawk's for the 7mm-08, after I was done hunting and packing meet back and forth, I took the scope off the rifle and kept it loaded with those for defense. I also had a big can of pepper spray usually. I saw a lot of grizzly bears, some as close as 40 yards but none ever did anything but stand up for a better look and then move along.
One of the years, I shot a caribou about 45 yards from the doorstep of the tent while eating dinner. Heard a snap-click noise that sounded like a brush fire just getting started and after a few moments a herd of them came up the hill, it was their hooves clicking together in the distance. Was probably about 40 of them all together, the females all walked by, they knew we were there but didn't seem to care. At the end of the line were 3 bulls. Had been there about a 5 days, and hadn't gotten closer than about 500-600 yards to any, so I shot the biggest one. After that we saw about a dozen bears over the next 4 days, within 400 yards of the tent, but they never came over to check the kill out.
I considered the 160's probably good enough for a really close shot on a moose, but never did it, and would have preferred to take something heavier if I went to specifically hunt moose or big bears, though I think 7mm-08/308 is fine for 100 yards or so, if your bullet selection is good. As it was, shots taken were 45-350 yards, ground ranged from flat tundra on the tops of mountains or several mile wide/long valleys of tundra to partially open forests, to near-rain forest density forest/jungle.
Something else to pack would be a fishing pole, esp if you are on the roads. The year we drove up, dinner was almost always caught on the side of the road, usually arctic greyling.
Bought a 444 AE lever gun to take, just as a hiking gun, but haven't had that chance.
And, I don't care if I miff off some TSA agent with that comment. 
