But if the parameters are within limits with thrust reduced, would it be prudent to use the APU bleed? One could argue that something led to the stall cause of which is unknown in the air so it's safer to avoid using the APU bleed. But what if you are operating at a performance limited rwy?
The problem of using damaged side bleed is smoke, some debris may come in the system. In the present scenario we are not sure about the damage to No.1 engine and due to performance requirement want full thrust from No.2 Engine. The situation is unusual. If we use APU bleed and if smoke comes in it will have to be treated as gunuine and you will land up doing smoke procedure. Not a desirable situation. Just do what would you do in an overweight landing with No.1 Engine shut with damage. Switch off No.2 pack. That's it.