By produce, I basically mean corn, squash and beans, of course
I can't answer your question, but I'm here to say; don't forget about wild rice.
Wild Rice, or Manomin is a staple crop of the Algonquian/Anishnaabe people. It grows in shallow lakes just south of the Shield and would certainly have been a part of winter storage crops. I have been told it was traded across the continent and to the tip of Patagonia, but I have no written sources for that.
[If you're like me, your only familiarity with this food is as long, hard black grains in an Uncle Ben's rice mixture. It wasn't until I moved to Anishnaabe territory, and got to try it properly prepared and cooked, that I came to understand how delicious it is. Fluffy and nutty-tasting, it's not what I thought it was at all.]