MakerBot Print is our newest print-prepration software, which supports native CAD files and STL assemblies,
allows you to interact with all your printers via the Cloud, and many other exciting new features.
No, there are no traces on the back side as far as I know. If we rule out the PCB than I am clueless.
And yes, each one of the four coils should be around 60-65 Ohms.
I've tried this motor on Chinese clone of DRV8825. Its regulation is tragic - especially for low current. EasyDriver should be much more suitable for this small motor.
It is strange that it is so much dependent on voltage as stepper driver is supposed to controlling current independently on voltage. There should be two voltages delivered to the stepper drivers. One Vref for logic of the driver 3.0-5.5V and another Vbb for the motor. Easydriver have its own voltage regulation so it can prepare voltage for logic side from load power supply, but also have pins to connect own 3 or 5V separately and some pads to switch between different scenarios. I think that for some strange reason your driver is feeding load power supply to logic part of A3967 chip, so it won't work above 5.5V as it gets overvolted. Strange it did not get burned yet when hooked to 12V. :D