Mr Optimistic
I am not convinced they knew/thought/suspected they were continuously stalled. Perhaps belief in the reliability of the messages and warnings left them and in a fog of doubt they tried to 'climb out'. Nose up and lots of thrust.
I would consider this as an option, if they wouldnīt have talked about the unavailability of a higher FL due to OAT just some minute before. And without AP and Athr the aircraft is easier to fly in lower FL than at max possible FL.
Itīs one of the first lessons learned with TS and buildups: Donīt try to outclimb one, it might rise faster than your machine is able to climb. Aditionally, there was no danger from below or from the FL they where flying at, which would have disappeared when flying 2000 feet higher. At least i dont know one.
An intentional climb is a "no option" for my thinking.