Drew,
I put the circuit in circuit lab. I was not exactly sure what the RS values for the filament winding was so I made an educated guess. I have also included two resistors to model the filament of the 12AT7. There are two problems you will face. First, because the the filaments have their center point connected to ground (pin 9) your stepper motor will not have the same ground reference. If the motor has its chassis shorted to ground this may be a problem. Second, you will not reach 16VDC, especially when the stepper motor is running. The specs for the motor you gave say that it should work down to 12VDC. If we can get someone to give us the detailed specifications for the 12.6 Vac winding we can get a better idea of the performance of the rectifier under load. Also, I used 1N4007 diodes but you can update the parameters for any diode. Here is the link to the circuit. You can open it, make changes, simulate it, and save it to your own workbench.
https://www.circuitlab.com/circuit/92f74h/stepper-supply/