Well, you do not choose your squad from any HQ!!!
The Kill-Team game starts with NOTHING. You only have UI 3 icons - your units choices.
So you press a SCaR button to chose one.
Something, the other players CANNOT know, until AFTER your squad is spawned...
I have just added you to the place where I have uploaded V2 of the Kill-Team win condition.
Have a look if you want, at this point it is VERY interesting. But it does not support MultiPlayer, although hit IS coded to support it.
The only thing missing for MP, is to see how a SCaR button click of one player, will translate to ANYTHING that can be communicated with the other players. Like deleting a squad (but this is UI functinality, not a SCaR command...)