Using higher N1 is not recommended for the reason mentioned in earlier post and it makes very little difference in any case.
The problem with air condtioning is usually due to clogging of heat exchanger, which needs cleaning or some other reason causing reduced bleed pressure. There are a few aeroplanes that have this problem and its really miserable for pax. Airline needs to be particular with engineering dept to pay attention to this important aspect in searing heat.
Packs are always on except for the duration of start.