John,
I am not a router guru, however, I do have substantial experience in the high speed machining of wood, wood composites, and some plastics. The issues/problems are same as with a router. I also own a few routers one of which, that by its photo, is the same or very similar to yours. We did purchase the machine used, thus I cannot compare it to a new one or your exact machine. That being said, we have discovered/confirmed that a rail set on one axis is not exactly parallel and that seems to induce chatter. Rigidity is key and our machine, 4 x 8, is lacking in that department. I have not experienced anything I would attribute to backlash.
Does your part have chatter on all sides? If yes, then I would explore movement in the part. I am currently machining .125 aluminium with reasonable results. We also, use a strobe to troubleshoot our other types of tooling. It is more difficult on a router because of the short linear movements, however, you can see tool deflection, spindle movement, chip load, and so on.
Again, check your hold down.