“How can I game the system”, regardless of the system, is by its nature a self-defeating question.
If there were some magical way to get your report ‘noticed’, among that, as you said yourself, millions of reports, then that would be the way everyone does it; which in turn means it would become one of the millions of reports again…
You may not have come here to hear this, but it’s the truth. We’re not here to blow rainbows and say there’s this one magical trick that all webmasters should know.
Yeah see, that’s the problem, there ISN’T any. You’ve done what you can do; file the report and wait for Google to get around to (maybe) doing something about it. You’re playing within the rules; the rules are slow, and retroactive at best.
But I wish good luck to you in fighting your good fight, which you definitely are doing altruistically as a crusade against the evil black hat seo’ers and not for personal gain…what color is that hat, again?
I have absolutely no idea what your situation in life is. In my own, I have learned that at times some goals are unachievable. The sooner I accept this, the sooner contentment. Not that it isn’t worth trying sometimes.
I can understand there would be some frustration.
2 related sites, say A and B
site B notices that site A comes before it in the SERPs for terms it wants A to come after it
site B looks into matters and concludes that site A isn’t “playing” fair
site B reports its conclusions to Google
after some time, SERP result positions haven’t changed
site B feels that enough time has elapsed that it is reasonable to expect the change to have happened
If the first is true and the two sites are related in such a way as they might be considered competitors then I suggest this thought.
“Some times it is easier trying to change what you can instead of working for easiest.”
If the first is not true and in no way could the two sites be competing for better SERP positioning then IMHO you have a right to be frustrated about not being Google. How much? How long?
Take the energy from the frustration and channel it into something productive. eg. make sure everything on your site is top notch. Or do some gardening or housework. You get the idea, something satisfying.