It sounds as though OP was on separate tickets, not simply separate PNR's (both BA and AA would each assign a PNR, even on a single ticket).
It is not the GA's decision. This is all handled in the software with the new overlay.
Without getting into the vagaries of each and every fare basis, if the fare basis is fully changeable without fee, then all OP needed to do was to have the change made. It is neither same-day standby nor same day change. This means that if, at the time the passenger requests the change, thee is one seat in J, the passenger gets it.
If the passenger was on a Saver redemption (which he likely was as he notes), then he may make the change, but goes onto the SB list for an upgrade just like the rest of the pack.
With all of the above said, I would have made the change before departure and not waitlisted. The transfer time (not a connection) was more than sufficient and OP was reasonably assured of no major delays by that point. Unlike BA, AA protects across OW-AA ticket transfers. Thus, had OP's inbound to MIA been delayed, AA would have rebooked him (perhaps into Y), but at least he would not have lost his ticket and he would have been no worse off than originally booked.