So what does it say about my level of FT addiction that I immediately spent 15-20 minutes on the post above...and only realized after finishing it that I had another booked passenger on the same flight, using points from an account that could actually benefit from the price reduction?
I went through the process again, phoned SWA again, and again (this time at about 1:15 PDT) the agent was able to adjust the amount of points charged. ^
An additional complication on this rebooking was that the points came from Mrs. ftnoob's account and the passenger was Mama ftnoob. To access the itinerary online to change it (without copy & paste from the Email confirmation) one has to log in to the passenger's account. When going through the change process, however, the change is refused at the last step due to not being logged in to the points-owner's account.

A log in hot link is offered, but (of course) it doesn't redirect to a continuation of the change process.