I don't use any, but have you thought about sewing something? Have you googled dining chair covers and looked at Images to see if you can find a style you like?

The chairs aren't currently upholstered, they are wood?

Is the wood something you would consider painting to fix the scratches and make them last? Painted chairs can look great.

I think some of the chair pads may come with velcro tabs instead of strings. Would that work?