6 output lines from the sensors, power, ground for them, 3 control lines for the coils. (I traced those also). Is that right?
Yes, that's right.
The Hall-effect sensors have four terminals, two of which come out on the connector (as you've found). The other two terminals behave like a diode and pass a small current through the device(s). On my CD-ROM motor, they were connected in series rather like a string of three LEDs. I added current-limiting resistors (100 Ohms at each end) and powered them from the 5V supply.
Good to hear about the two other DC motors, too!