Upper Reward is in G clas,, you will not be able to see this online unfortuantely.
Premium Reward is in V class if I recall correctly.
As for changing inventory to get award seats, it really does help if you are a GOld and a frequent customer at that. However you can ask the agent to speak to their supervisor to speak to revenue management, but the supervisor will make the call to be honest whether to call revenue management. You could tell them that you can see there is good availability in Z class and if they could swap one toa G for you. If there is no Z class avail then don't even bother, you'll get nowhere.
It may help to remind the agent that there are normally only 2 G class reward seats made available, and the J section holds 48 on the SFO route.
Thanks,
Richard