The AAIB conclusion to this report "the pilot operated the aircraft in an autopilot mode which left it vulnerable to a stall..." seems vague in its intention at establishing an actual cause.
According to the report, on this aircraft type the pilot has two climbing/descending flight director (not autopilot) modes to choose from: Verticle Speed and Flight Level Change. Both, according to the report are acceptable means of achieving the job (according also to the AFM reference) and both are fully certified as safe for operational use. The pilot reported that in FLC the plane would hunt and this is the reason for using VS, presumably in VS the occupants had a smoother more consistent ride, or perhaps the pilot found it easier to comply with ATC Verticle speed requests by using VS on this day or previous. Perhaps the pilot found it easier to maintain the RVSM required 1000 feet per minute or less within 1500 foot of desired altitude (albeit above RVSM). It doesn't really matter in my opinion why the pilot chose to use a perfectly usable flight director mode to achieve the aim, the fact is that he/she failed to monitor the aircraft during a critical phase of flight. Verticle Speed and Flight Level Change are just proverbial tools in the tool box and neither is more dangerous than the other in an unmonitored aircraft. To cite the use of VS mode alone as the number one cause seems like deferring attention from the actual reason and that can only be non monitoring by the pilot, otherwise one could blame gear up landings on the act of retracting the gear in the first place, what a dangerous procedure retracting the gear would be if the pilot forgot to extend it again before landing due to destraction.
Slightly hypothesising here but in theory if the pilot were to climb in FLC at a fixed Mach number then, as the aircraft climbs the indicated airspeed (IAS)will reduce and the same result would have occurred (this presumes obviously that the aircraft would have an excess of thrust to maintain a given Mach Number to the target flight level, otherwise if unmonitored it would level off and possibly start descending!).
The AOA not working correctly was bad luck and didn't help the pilot by pre alerting the stall correctly but again, if the speed was being monitored then this situation would not have occured. All aircraft have a minimum drag speed (VIMD) which occures usually at the same approximate speeds for given conditions that the pilot should have been aware of. If the AOA indicator had been observed stuck reading .6 then a vigilant pilot would have noticed this not working and relied on his/her experience of this aircraft type to maintain a 'not lower than' speed. Flying below the VIMD is probably why the IAS kept dropping beyond what the pilot considered to be normal.
In my opinion, and it is just an opinion and not based on fact, either VS or FLC could have yielded this event and along with the AOA indicator were red herrings. This plane was clearly flying too high and too slow for the given conditions and the pilot took his/her eye off the ball.