With transporting firearms to Canada, the best thing I found was to find a direct flight to Vancouver. In my case I flew Air Canada which stopped at Honolulu to refuel only. Even though passengers and carry on bags had to go through US immigration, checked baggage did not. It stayed on the plane. I di ring the ATF in the US months ago and they said that there was no permit for what I wanted to do, but, so long as I had my Canadian hunt contract, I'd be fine. (didn't have to test this theory out thank god).
On the return from Vancouver, US customs are actually set up at the Vancouver airport. So you actually have to go through them before you check in your baggage. The US customs officer just asked if I was taking the rifle back to Australia with me and then asked how my hunt went and what calibre rifle did I use!!!
These direct flights are definately the way to go, and more of them will be happening soon. I understand that Air NZ will be starting non stop to Vancouver in November with Air Canada also starting up in December, I think!!

Hope this helps. Don't worry, I had sleepless nights when trying to plan all this!!!

Cheers,
Mark.