Priority is based on elite status, then fare or category of ticket. What you should do is check prior to the 7-day SE upgrade window to see if any D-class award space has opened up [someone cancelling, etc.] and again at the 72-hour Elite window. At the gate, an award does have the same status as a full fare ticket, but that is not often a consideration in upgrading.

How far out is your flight? If it is several weeks or months, you will find J is fairly open since these fares are not generally purchased that far in advance. If it is a week or two, then keep checking to see if any D-space opens up. What is your elite status? I suppose you are not eligible for waitlisting.