I had the very much the same problem, until our fridge died and the replacement I bought came with one of those temperature and humidity controlled vegetable dr

I had the very much the same problem, until our fridge died and the replacement I bought came with one of those temperature and humidity controlled vegetable drawers. I hadn't paid it any mind, since I assumed it was just some marketing gimmick. But much to my surprise, those things actually work — vegetables easily keep three times as long in them. Doesn't help with the buns, of course.