Nice idea Mann, similar to the Aerodrome (I think it was the Aerodrome?) in some ways although sans cargo mechanic. One problem I can see with your reasoning although not with the format is:
"Obviously there is a kill limit so teams will be advised not to team up with other teams in game. Your kills, your score."
Basic game theory, GoI massively rewards teamwork, especially in 4v4, unless you know your enemies are going to split up you are well advised to form a spontaneous 4 ship team since getting half the kills in a 12-10 is going to get you way more point than in a 12-3 game. Since forming a 4 ship team always increases your likely kill rate it is a stable equilibrium, you wont get teams splitting. Only exception is if one team was so good they thought they could carry on their own, then they should try to get all 12 kills.