If you do not want to deal with cardboard spool rings, here's another solution for you. Rip off the two sides of your Jayo cardboard spool, and slide the center into the wide portion of the printed spool, and then slide in the narrow portion and twist to lock it in place.

Take note that there's a notch on the wide portion of the spool, which fits into the small hole that is present on the Jayo spool, this will allow it to lock in place and not move.