Those few pieces would be easy to just remove and replace with similar fabric. IMHO, I don't think it has to be a perfect match. repairs are part of the history of the quilt.
You can cut the bottom and top edges to be straight also, just like the sides. As far as the fraying edge, I would use a strip of light weight iron on interfacing around the edge, maybe about two inches wide. Then finish with border/s of your choosing. The interfacing will not interfere with finishing.
What a great find. I love to do this kind of work on found treasures. Keep us posted as you progress with this project.
peace