You don't just "Cross Through" Alaska it doesn't work like that. Even if you were to walk non-stop from the Bering land bridge to the boarder of Alaska, the shortest distance is over 800 miles. Now please note I said walking, not walking down a crosswalk, this is serious buisness walking.
As obsticles you have:
Angry Wildlife
Swamps
Rivers
Mountains
Mosquitoes
Lakes
Forests
And that's just in the summer time when its warm.
If you had good hiking gear, and were clinically insane, I suppose you might be able to make the trip in about... 4-6 months.
But, the ancient people really didn't give a damn where they were, they just wanted food and a nice place to stay. Considering they had no idea what else was out there I'm pretty sure they weren't making a mad dash for the boarder.
If they found a plentiful food supply they probibly didn't move from that spot. At least not untill A. The food ran out, B. They became over populated.
So it prolly took people on the order of several Melennia just to get out of Alaska's boarders.
So all your Indian's are Canadians is a bunch of bullox.
If you are going to even bother extrapolating since we went through A so we are A'ians, whats the point? It would be far more accurate to say we originated from Mesopotamia, Africa, and Europe; than any place that people were slowly migrating through.