Before You blame this idea as too radical, I just want to state - I understand, that probably I go to far with this, but would be great, if there is at least mod available for it
In PP soldiers can move for 1/2 AP or 1/3 AP, so I guess, there is a hidden mechanism, which works with higher numbers in AP system,
4 AP just want to look familiar with modern XCOM and Gears Tactics, but does not fit Phoenix Point well in my opinion.
I would suggest to increase AP system from 4p to 8p, this would allow to fix the heavy weapons use and open further balance options.
Heavy weapons (HW) simple needs AP’s value between Assault riffles(&Shotgun) and Sniper Riffles - HW needs more mobility to use. but if they cost 2AP (and shot 2x per turn), would be OP
general AP system would be increased from 4p to 8p
assault riffles 2p -> 4p
sniper rifles 3p -> 6p
heavy weapons 3p -> 5p
So Soldier with HW would finally get necessary mobility, but not too much and would not able to shot twice per turn