The fact that it works with Repetier is useful to know but I'm not going to study the Repetier software - it is much too complex.
I think this
I run the Z-axis stepper motor, then change nothing but the pin numbers (which should cause the Y-axis stepper motor to run), then record the Y-axis stepper's stillness,
means that when you change the pins for the Z stepper from those for Z to those for Y the Y stepper does not move - even though the exact same code made the Z motor move when the Z pins were used.
I am not familiar with the "RADDS v1.5 board " but one possibility is that you need to pull the enable pin LOW to get the driver to work. (And if that works, don't ask me why it is not also needed for the other axes 
)
Am I correct to assume that the pins for each motor are defined by the RADDS board?
Are you sure you have the Y pins correct? For example step and dir might be mixed up?
...R