I have tried running the motor without the collet and nut, and it seems to run slightly faster and more quietly. I tried removing the set screws you describe, but could not get the collet holder off with gentle prying, which is why I asked. Frankly, when I received the spindle I was surprised how thin the spindle shaft is; it seems like that's a weak point in the design.
I'm using a power supply I already had and upgrading from the dremel, so I don't speed control yet (I'm waiting for it to be available on the inventables store).
... after a little tinkering ...
And maybe the "weak point" was intentional? Using a dial gauge and some brute force, I was able to bend the collet back to ~1-1.5 mil runout on the tool bit and rerun my test pattern. Here is the result.
From left to right, the vertical traces should be 10, 12, 16, 20, 24 mils. A quick check with some calipers shows that the actual board traces are about 1.5mils wider than nominal, but that is likely because I was cautious with the mill depth. Compare to before fixing the runout, where the 10mil,12mil, and some of the 16 mil traces were completely gone.
P. S. the "thermal vias" should have been exactly centered on the square except for operator error (changing a bit and then "go to zero" requiring an e-stop to prevent the bit crashing, and losing a little bit of registration in the process.)
If you're having problems with fine traces being obliterated when milling a pcb, your spindle may have large runout. Just using your hands and a dial gauge you can bend the spindle to minimize runout. It also helped to reduce vibration.