Air will help. If there's a way to let the stuff dry out before you put it in the new bin, that would make a big difference. But I understand about the smell and maggots. If you have to put it in the new bin, you might want to go as high as 80% on browns -- even if you have to leave some of the old stuff in its bin before you can get more drys (newspapers, paper bags, etc.).
ETA wouldn't hurt to find yourself an odor mask, either, with a charcoal filter. Not that expensive. Decent hardware store/big box home improvement center.