Your solution still has the same problem.
The video they show you (in Kings County anyways) when you come in for jury duty shows historical cases where that is exactly what happened: a large group of judges unfairly sentenced innocents (to death, IIRC).
I was selected to a jury on a murder trial (got excused in middle, but that's another story). The jury was not made up of idiots at all. Just average lower-middle class Americans of all kinds of backgrounds and ethnicities. Although the other guys on the jury seemed more interested in getting an up close look at the knife that killed the guy than figuring out if the defendant was guilty :-)
In the jury selection process, a lot of people tried to turn themselves into racists, cop haters, and all sorts of things mentioned on this thread to get off jury duty. The judge didn't care for all their excuses. Basically, if you're relying on those excuses, YMMV.