Weve been using the 17 hmr out on kodiak for foxes. SO far it has been awesome. Farthest shot to date was probably a 100 yards. Good clean kills, no damage. Other than that I think the 222 is a good choice. The hornet would be another good choice, but your limited to about two kinds of factory ammo with that. Of course there are only about 4 kinds of ammo for the 222. Guess you better take up reloading too LOL with foxes I think you want to keep bullet velocity down. Lots of bullets these days you buy over the counter for fast 22 cal rifles are highly fragmentable and seem to cause alot of damage on pelts.
Here is a good piece of advice. Buy something cheap, reliable and go out and call some critters. I wouldnt stress too much about alot of bullet or rifle choices. Concentrate on calls and getting something to come in.
If I were you Id keep using that 17, and spend the money on a foxpro with remote. When I got my foxpro, my success practiclly doubled. Not alot of people have one, and the sounds are pretty unique and the preds seem to respond to it very well. Make sure you have a woodpecker in distress, that sound is MONEY!
Alaska (the road accessable part), for the most part, I think, sucks for calling. We dont have near the population of predators that the lower 48 does, and the ones that we do have are pretty timid and call shy. Couple that with limited access, and lots of calling going on with what access there is and you come out empty handed 99.1% of the time.
Ive pretty much given up calling around the mat valley, kenai areas. Im still interested, I just go somewhere where they are, even if I have to buy a ticket.