I think Gambit is fine the way it is.
Also, your suggestion doesn't seem very friendly towards that one quest step for Malfeasance where you, or your teammates, need to kill 4 people in 1 invasion.
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Well I would think it would reasonable to have to get a couple kills with a primary and secondary, then have the option to finish off the other two with a rocket. And with my suggestion of a buffed overshield and increased invade time, that quest step would still be attainable. Using a primary isn’t impossible, it just takes calculation on the invaders part rather than mindlessly running in head first with 1k.