In the statement that:
Mcrit does not change with angle of attack, it is the speed at which somewhere on the airframe the local flow will go sonic.
The part that says:
it is the speed at which somewhere on the airframe the local flow will go sonic.
Is correct.
But the part that says:
Mcrit does not change with angle of attack,
Is not correct.
When we are flying at Mcrit the fastest airflow at any point over the airframe is Mach 1.
This (Mach 1) is the sum of Mcrit + the greatest acceleration over the airframe.
Rearranging this equation gives us Mcrit = Mach 1 - the greatest acceleration.
If we increase the angle of attack we will increase the acceleration over the aircraft. This means that we do not need to go so fast to achieve Mach 1 airflow at some point over the airframe.
So increasing angle of attack will DECREASE Mcrit.