Knitting on hold. New project? How to re-cane a chair seat!

Yes, my knitting has been put aside. With the kids heading off to Utah, they have decided that they want to take everything with them that has been given to Jacquie by her grandmother because (as Jacquie says), "We're not making another U-Haul (or Penske) trip!"
So...since she is getting the bedroom set that my grandfather bought - probably around 1920 - I have to get it all shined up and pretty! The biggest issue is the condition of the two chair seats. They need to be re-caned and I am trying to locate a supplier of cane sheets and splines (yes, "spline" is a word! It's the thin strip of wood that encircles the sheet of cane):

Example:


Jacquie's dresser:


Headboard:


Washstand:


Side table:


Chair back:


Chair seat: