Brandon Badger (https://plus.google.com/114800310452543164210) is the Project Manager. He's been running contests on Google+; submit artwork relating to ingress, stories, etc. hashtag them #ingress, and if he like it he'll reshare it and give you some invites.

I didn't even know about the contest when I wrote https://plus.google.com/110847385311561387629/posts/ePGPdJCS..., but apparently it got to him anyway and he gave me some.

Check out his feed for examples of the things he's reshared.

You may be a misguided pawn interfering with the advancement of humanity, but that was awesome.

Don't know about quick. It took me about two weeks to get an invite. Just submitted my email address.