I guess the third time is the charm. This time I pointed out the T availability on EF (I don't know if that made any difference) and the agent I talked to this last time was seeing the exact same thing I was seeing on EF. He went ahead and tried to book it, said there was a problem and then said he was going to try something else. About 15 seconds later he asked for my companion's information and verified mine. I just got the email confirmation that it went through.
WOW, what a major PITA.