If I may throw in a few thoughts:
The natural phugoid period is approximately 0.23*Vkts TAS, that is about 28 seconds at 120 kts. If you are looking at a transition period of say 3 seconds that is only going to be one tenth of the phugoid cycle and I doubt it you would see much variation in that time. The terms AI have put into alphaprot to stabilise the trajectory also have a significant short term effect, basically by limiting the allowable AOA if the speed is decreasing but also there may be (probably is) a pitch rate term to add damping to whatever short period motion is associated with alphaprot.
WRT the discussion on what happens transiently if you increase thrust at alphamax I can offer two partial explanations; the reality is probably some combination thereof.
If you add thrust you will, of course, get a nose up pitching moment. In steady state conditions to maintain AOA constant this additional pitch has to be balanced by a nose down pitch from the tail. This means a reduction in tail download so there will be an increase in TOTAL aerodynamic lift even if AOA stays constant. In addition of course you will get an increase in total vertical force from the vertical component of the increased thrust.This is why Vs1g is established with idle thrust.
In the transient the increased thrust will cause the aircraft to pitch upwards and the EFCS will react to this changed pitch rate by applying down elevator (or more accurately will reduce the amount of up elevator) and the mechanism described above will come into play. So the total vertical force will be increased a little by increasing thrust even at constant AOA and airspeed.
The other explanation, which I think would be more powerful, rests on the fact that alphamax is not a 'hard' limit. The generation of wings we are discussing does not have an abrupt 'stall' [I cannot answer for the latest generation with sharklets or curved up winglets/wing tips; they may well have different characteristics]. The likes of the A320 start to have flow breakdown somewhere near midspan and this spreads outboard and inboard as AOA is increased above this point. This is true for both the clean aircraft and with flaps deflected. It is the buffet produced by these separations that becomes the limit to useable lift. In effect alphamax is almost a subjective limit, although formally it may be defined by the level of buffet 'g' at the pilot's station reaching a set level.
Now the aircraft is not going to fall out of the sky, or the simulator come off its mountings if the buffet temporarily goes up a little - assuming that is that the simulator has realistic buffet reproduced anyway. Consequently, there will be a margin of AOA available, but not available for general use, beyond alphamax.
Any closed loop control system will need to preserve some margin between the nominal system maximum and any genuine physical limit. The margin will depend on the nature and consequences of that physical limit. If it is a potentially catastrophic 'cliff edge' limit then the margins will need to be carefully set but if it is, as here, a 'soft' limit then one can be a little more relaxed.
To judge by the Gordon Corps video, AI are quite happy to see AOA go as high as 17 deg with full flaps even though the maximum usable AOA is set at 15 deg.