Refrigerant pressure is found in the ECU section - its here that its used to compensate the engine speed, torque output and also battery charge rate .
In order to fill the system yes - unfortunately the gauges hung off the LP port is the only reading to trust. However - the high pressure line's measured pressure (your sensor's purpose) can help you check the guys are not overfilling the system and thereby again screwing you.
If you saw -40C temps on there I guess you have no or very little refrigerant in the system (low pressure refrigerant = low temperature on the P vs T chart) .............. lets hope as you say you now have a situation where a low refrigerant pressure is simply disabling and protecting the pump.So just imo - I don't know anybody that can hang a gauge of the AC system and come up with a statement as to the weight of refrigerant currently in the system ...................

Also imo only - again - how the heck did they fill the system properly without the pump kicking in ?:crazy:
On your driver's door pillar there is a sticker with your Vin number on it - its the 4 characters found in position 4,5,6, and 7 of the Vin number - mine is eg JM1B - yours will be something similar like JMxx