It would seem that based on the vectors, and if the A/C was within CG limits, positive pressure at elevator wing surface will induce pitch down moment, thus not maintaining positive pitch angle. There is no elevator shadowing from main wing components (which is the definition of a deep stall, really). Could a transport category aircraft be certified if a deep stall condition can be produced simply by stalling in a double flameout / power idle? I don't think so.
EDIT: Unless spinning of course, you are correct. It took an incredibly unfortunate conspiracy of fluid dynamics to get them into this state!