Thanks very much for your reply.
Yes, that's what I meant. If I replace those Z pin numbers with the X pin numbers, the X stepper runs, but when I replace them with the Y pin numbers, the Y stepper doesn't run.
I wish I could say that pulling the enable pin LOW worked, but it unfortunately didn't make a difference 
Since the drivers are wired into the RADDS board, which stacks on the Due, yes, the RADDS board's circuitry determines which Due pins correspond to various driver pins. I'm rock-solid certain that these pins are correct and not swapped around; I contacted the manufacturer to make sure.
In all honesty, I am quite stumped. Perhaps the board is defective--maybe Repetier does something that shouldn't be necessary if the hardware is fully functional, but provides a fix if there's a break or problem somewhere (in my case, in the Y-axis).