Just played Laser Squad out of curiosity.
It was hard and I killed my own dudes.
Now that I have context to understand the videos I believe this will be fun.
As an alternative suggestion, you could give radically different effects for different shot types. For instance a snap shot could provide a free move, simulating a unit hustling from cover to cover. An auto shot could have a low chance of actual damage, but suppresses a target making it easier for other units to outflank it or attack it.
I like this idea. Suppression could sap an opponent's AP?
I imagine a scenario where one human flanks and suppresses an alien that is covering a door. The doorway is now free to move through, as the alien does not have enough AP for an attack of opportunity.
Alternatively, some guns could just have a suppressive effect whenever they are shot. Robots could be immune to suppression.
I am new to these kind of games so do not value my opinion.