Thankfully the other F-4 guy (Franzl) has more time to post than I do, but I'm in full agreement with his analysis.
Full nose up after the stall, was simply an attempt to stabilize the aircraft's pitch attitude by a pilot who didn't understand WTF was happening.
There is sufficient reason to attribute the initial nose up leading to the stall as coming from the roll instability leading to inadvertent nose up inputs and the tendency of the aircraft's pitch channel to mathematically integrate those inputs. (For those who did not take calculus, it means add them all together). When did the initial nose up occur? Answer: When PF was fighting the roll problem the hardest. Did he have time to formulate a strategy of setting a nose up attitude? I doubt it. His computing power had to be focused on the roll problem.
Why doesn't the aircraft stop trimming in Alt2 Law when approaching the stall like it does in Normal Law?
More than likely, the engineers couldn't figure out a reliable way to do it. With stall AOA a function of Mach and gross weight/configuration, they didn't know how to make the Mach correction without airspeed inputs. They really should re-examine this more closely.
- You can likely make a fairly good Mach approximation from inertial data. With that data, altitude data, and a safety factor, they could stop the trim from running up to the limits.
- By considering alternate sensors for determining a stall state, they could probably stop trim from running up despite what would seem to be reasonable AOA at lower altitudes. What happens to the airflow over a wing during a stall anyway? Don't you think we can make a sensor to detect that state? I do.