Happy to report that I called to request a TP using points from my wife's account. Got a knowledgeable CSR after the second call. She transferred 270K points from my wife's account into mine and then 120K miles into my Southwest account -- and issued me a 7 night certificate valid for one year.
Two days later, Southwest sent me a message telling me that I qualified for the Companion Pass.
Did your wife have to get on the phone too? If so, what information did she have to provide?