I got a reply from Custom PCB:
Yes, Eagle generates lines below 6 mils all the time. It is always up to the PCB manufacturer to fix it up to their minimum line width. So we don’t check against that because it is not something that designers can easily fix with their PCB software. But we do warn customer about silkscreen problems if their text is too small to be legible after increasing the line width to 6 mils minimum.
I just finished re-laying out the constricted ground wire. The narrowest constriction is 0.25″ now, but only for about 0.1″. The thermal calculator can’t handle constrictions well—it wants to analyze under the assumption of an infinitely long wire 0.25″ long:
The trace width calculator uses empirical formulas based on long traces with no special heat sinking. … The trace width calculator is more geared towards long traces. Short traces with heat-sinking to planes do not get as hot.
It predicts a 30ºC temperature rise, but since I have a lot of heat sink nearby, I think that the temperature rise will be well under the usual 10ºC design guideline.
I also checked my vias with http://circuitcalculator.com/wordpress/2006/03/12/pcb-via-calculator/, which says that 27 mil holes with 1mil plating 62mils long should have a resistance of about half a milliohm and be able to carry about 3.4 Amps, so 5 such vias should be enough. I have 11 or 12, which should be plenty.
Figuring out minimum trace width for a given voltage drop or power dissipation with http://circuitcalculator.com/wordpress/2006/04/20/find-pcb-trace-width-based-on-power/ might be useful in some other applications, but I’m less concerned about IR voltage drop than I am about temperature rise.
So, after I’ve gotten some sleep and had a chance to see if Gabriel or Steve can check my design, I think I’ll be ordering from CustomPCB.