some messages concerning the aircraft’s configuration such as stall or overspeed warnings are not recorded
Thank you for pointing out that BEA quote HN39. If such warnings existed, that would have invalidated a Vmo/Mmo protection pitch up scenario. I was having trouble finding an ACARS reference on the subject. The only other thing that might contra-indicate such a pitch up is the rudder limiter position which probably would have locked at the polled airspeed indication existing when Normal Law was abandoned.
I wonder what BEA used to exclude such a pitch up scenario in the process of setting the search area? To me, being left 20 degrees nose up at FL384, M 0.66, at night, with no visible horizon and on the outskirts of a big cell, with no valid airspeed, in a fly by wire aircraft that has just shifted to Alt2 Law seems a bit hairy.

Any delay in pushing the nose down would almost certainly result in a stall, particularly without AOA indications to see how the wing is flying. (Just had to put in a plug for AOA indicators

).
If AF447 promptly entered a stall, it might flop around a bit initially but as long as the stall remained, it would likely cause further deceleration until the AOA was quite high and would then result in a stable attitude pretty much along the lines of the impact attitude described by BEA. The flight path over the ground would likely describe an inward spiral starting from an initial circle of no more than 10NM diameter and would be fairly close to the LKP.
It seems that there may well be valid potential to searching the "donut hole" in the last search pattern.