I think reports filter themselves to a large extent. Consider: while the Tribunal was active, the report system built cases based on the ratio of reported games to total games over the period (called the "report density"). Specifically, it took a report density of 12-25% to have a case formed.
Now, I'm willing to admit that those numbers may have shifted some, but I see no reason to believe that the basic function of that system is significantly different. Which means that any reports to accounts that fall under that amount are ignored entirely - and considering that some 75-80% of the community never has a case built against them, that could potentially add up to be a fairly significant number of reports.
Of those that remain, I see no reason that a sufficiently sophisticated chat-detection algorithm can't validate the majority of cases. Combining that with spot-checks of a semi-random selection of cases would allow for an extremely accurate system requiring a relatively small amount of manual oversight while still managing a very significant throughput.