Alaska Airlines has an ammo limit of 50lbs for a fact. They also allow 3 bags at 50lbs each.
As for transported across Canada: "Firearms are classified as non-restricted, restricted or prohibited. Visitors CANNOT, under any circumstances, import prohibited firearms. ALL handguns are either restricted or prohibited. Visitors may temporarily import restricted firearms provided they get an Authorization to Transport (ATT) in advance from the Canadian Firearms Centre. Non-restricted firearms may be imported only for sporting or hunting use; for use in competitions;
for in-transit movement through Canada; or for personal protection against wildlife in remote regions of Canada (excluding national parks) as long as the customs officer is satisfied that the circumstances warrant the importation of the firearm.
Non-residents can import 200 rounds of ammunition duty-free for hunting purposes, or up to 1,500 rounds duty-free for use at a recognized competition.
You must declare all firearms to the Canadian Customs officer and complete a Non-Resident Firearm Declaration Application Form ($50). The customs officer may check to ensure you have transported the firearm properly. Non-restricted firearms being transported into Canada must be unloaded. If left unattended in your vehicle, the firearm must be locked in the trunk or a similar compartment of the vehicle or stored out of sight.
Restricted firearms must be disabled from firing (e.g. with a trigger lock) AND locked inside a heavy-duty, opaque container.
If you have declared a non-restricted or restricted firearm but cannot meet the import requirements or do not have the proper documents, the officer may allow you to remove the firearm from Canada. Or the officer may hold the firearm until you can produce the correct documents. Prohibited firearms, weapons and devices will NOT be returned to you. Anyone who fails to declare a firearm or illegally carries a firearm into Canada is subject to a number of penalties, including criminal charges and/or seizure of the weapon and the vehicle in which it is carried."
This doesn't really say how much ammo one may be allowed to bring through unless they imply that would fall under importation which means very little.
Bottom line, you are most likely going to have to ship everything unless you take the ferry. Shipping in and out of Alaska as well as importing ammo is expensive -
get used to it, that's just Alaska and part of the deal. If you can spend that much on housing, you can afford to ship your goods. A one time beating won't kill you, you just won't like it.
We normally import ammo using ocean freight, there is no ground shipping to/from Alaska. Any way you cut it, it's going to cost you. It's part of what keeps out the riff-raff.