You wrote:
"The way I see this scenario is that the alerts you mention, except perhaps the stall warning, would only have been triggered when the situation had already become serious."
Exactly!
But the validity of the statement requires that the aircraft was on the GP (or close), which I - like you - believe it was. (from approx. 1000 ft.)
brgds
Note: Link given in #728 has a lot of information:
The Aviation Herald