Three Bears supermarket in Tok is a good stop for us. Cooked and/or frozen items are usually less of a concern than fresh items. I have crossed at times when fresh eggs are not allowed but hard boiled, peeled ones in the fridge were OK to take across.
I lived in rural Alaska for 25+ years and never thought the prices in Alaska were any real difference than in northern Canada. We often stock up in Whitehorse due to them having several nice supermarkets, with good selections. This and a stop for needed items in Tok, will get us to Fairbanks or Anchorage.
Depending on many factors, such as where you live, your work history, etc, food questions may not even come up in their questioning. I have a bit of law enforcement type work history in my past, and once that info pops up on their, either side of the border, computers, that is all they want to talk about.
Normally the day before we cross the border, I try to get online to see what is on the prohibited list. Then we will make meal plans to use up those items. I will cook meat products I purchased in Canada, and freeze them before crossing into Alaska. Never had a problem with that method. As long as a person is honest, they may have to give up some food item, or pay some extra duty on the item, such as booze, there just isn't any serious repercussions, unless you have firearms or illegal drugs not declared.
