Hasn't your store put a limit on paper products yet? In our area you're limited to one (or some stores) 2 items of tp, paper towels, paper napkins, etc. No one's really complaining about it (except possibly a few hoarders or scummy re-sellers) and I've not heard of any scuffles in the aisles.
I think that some dairy products also have limits of one or two. It all makes sense to me?
They also have to early hour for seniors. I was surprised to only see maybe 2 dozen people, a few with masks. Most were pleasant and the cashiers were still chatting with some of us regulars as we checked out. The store workers were going "full blast' re-stocking and you had to work around boxes, etc., but all in all it was a pretty civilized experience.