Right, I forgot this point. ULN2803 COM should be allowed to swing to double power supply, e.g. by adding a 12V zener diode between +12V and COM.
But an unipolar motor will still work at lower speed. Particularly the voltage measurements reported in the post can't be explained by clamping diode effects. It sounds like a much more trivial problem.
In any case, the main question is about bipolar stepper drive. Whatever's the problem with your unipolar motor, the bipolar motor doesn't work with ULN2803.