ya the 15" is a bad size for the CJ. The only way to do this would be leave the far right pinch roller some where over the right roller. Set your 15" material so the left edge is on the 3rd roller from the left and use the center roller on the 4th roller. You will have about 2 inches of vinyl to the right of the 4th roller. This will hold the vinyl in place and use those two rollers to feed the material. Then you need to trick the censor into seeing material from the right side roller to the edge of where your vinyl starts. On the CJ taping over censors does not work that well as it moves media back and forth over the censors to detect length of material. What I would try is to set a scrap of any material thats about 15" to 20" (could be backing paper from other jobs as long as it longer than the job you want to cut) and set this piece in the CJ to the right of the 15" vinyl that you are going to cut. The scrap will move parallel to your working vinyl and thus let the censors detect as they should. *** just make sure that you manually set the base point to where the working vinyl is otherwise you will start cutting on the scrap.
Key is to be able to use at least 2 rollers to hold your material you are cutting. The other scrap can slide around a bit as long as it still covers the front and back censor, otherwise it will stop cutting and think the media ran out.
I'm sure this is clear as mud......