That sounds like quite a collection! This kind of thing might work.

I have a hutch that has small groove along the back that allows for display of plates. I have also seen shelves with same groove. I can't take picture because hutch is in storage while we redo downstairs. I know the shelves are called plate shelves. I also have large collection, but I rotated which oblates I displayed at any one time. I think it was Bradford Exchange that had frames which were beautiful (I really dislike plate hangers, plus they can damage plates). I don't know if Bradford is even still around. Try Googling plate shelves.