All your detailed comments on how the FPV is working are certainly interesting, but as the ACARS messages might suggest, the AF447 crew has probably tried to get the help of that bird to stabilize the situation ... but the bird was just INOP !
The only available tool was a pitch and a thrust setting.
As PJ2 said, the bird is not usually used in routine descent or cruising phases. Its utilization is more dedicated to approach phases, a great help, almost magical to stabilize an non precision approach, a bit like having a flight director on its own.
To think that the bird was selected at FL350 makes me believe that the crew was looking for some kind of certitude. The FPV red flag was probably not what they were expecting ...