I bought a set of these Boye Needlemasters a few years ago. My BFF has a vintage set and uses them almost exclusively, hours per day. I liked the finish on the needles so much, plus the great colors, that I bought then on a post holiday Jo-Ann's sale.
The only way I can use them when I need that Boye finish is to put the cables in boiling water in a dish, let them soak a while. It helps.
However, my cables are only two years old, relatively new. Maybe vintage cables are more brittle, less accommodating.
Have you tried the hot water soak?
My BFF doesn't keep her cables coiled up in the case unless she travels. Otherwise, she keeps them suspended, hanging, with a needle tip screwed onto the end. It minimizes kink/curl.