I think the best thing you guys could do is to develop a joint role play saga with another faction you can work with and play it out for the public. A "one of" thing.
Gives people a chance to see you perform.
Might change a lot of minds.
The only other thing I think you guys need is a "rules of engagement" so you don't look like pvp types over killing.
The "Flying Circuses of WWI" had a gentleman's code of honor and ethics that showed their professionalism. Some same sort of thing would do for you.
Early in his career, Richthofen was criticized and looked down on for always taking easy kills--reconnaissance and bomber kills.
Later in his career he himself expressed regret for having indulged his reputation so zealously with such things.