Source for Replacement Dobby Cords?

I am finally getting my PDL set up and some of the dobby cords are worn and need replacement.  I have a (very) old PDL the uses braided cord, not wire.

Does anyone know where I can find the right cord to replace the dobby cords?  I have not called AVL yet but they do not have have them on their web site. (Plus their prices are so high!)

I was told to use deep sea braided fishing line (tarpon line) but here in Colorado there is not much demand!  I tried searching online and found lots of braided fishing line but the diameter is not usually listed.  My existing cords are 1/16 inch (0.0625) in diameter.

Has anyone else come up with a good way to to replace these cords?