When booking onto another carrier, unless you've paid for J you're only going to be entitled to Y on the other carrier. A supervisor will sometimes override and put you in J on another carrier if you've used a GUC/Miles to upgrade. However, there's nothing that requires them to do it.

SDC has nothing to do with anything here. That policy only deals with switching to other DL flights. There's no "money" lost to another carrier in allowing SDC. Rebooking you onto another carrier in J does incur costs.