I spent a lot of time in the Nome area. I was CO of a NG Native Company out of the Nome BN.
As to shooting moose, my opinion is go with the 'o6, with good quality 180 gr bullets. They are more then capable.
As to Nome area. Not a lot of roads, I dont know if you're a foot or planning on hiring someone to fly you out.
The Seward Penn. has some mountains but mostly rolling brush covered hills. Best bet would be glassing the tree (brush) line another river/creeks until you spot one, then figure out a stalk.
There is a lot of country out there, to be honest I've done most of my traveling on skis.
I havent been there in a long time. Back then you had to be careful hunting on native lands.
I dont know where exactly your suppose to hunt, but If I was to hunt there, I'd hire a 4 wheeler and hunt the Taylor road. Then if time permitted, take a boat to Brevic Mission
then hunt the wooded are east of there.
Its been 30 years. When I lived up there I went out with the natives but I really didnt hunt my self.