I tried moving the piston - there was resistance, even with the bleeder open. I didn't force anything, and perhaps this was for the best. I just found this little tidbit; while it doesn't specifically refer to the 3, it certainly suggests that there's more to the job when the electronic parking brake is involved. Excerpted:
Mazda integrated EPB system caliper servicing without a scan tool
Mazda provides a non-scan tool option for 2016/2017 CX-5s to retract the integrated caliper back for service, that is very similar to the process for Fords. This procedure can be followed to enter maintenance mode.
Entering service mode:
1. Switch the ignition ON, and don’t touch the brake pedal (the engine must be off throughout the procedure).
2. Release the EPB. Note Steps 3 and 4 must be done within five seconds.
3. While simultaneously pressing the accelerator pedal down fully, and pressing the EPB switch and holding both, switch the ignition OFF. You need to hold both the accelerator and EPB switch in this position during the next step.
4. Switch the ignition ON, while maintaining the depressed pedal and EPB switch.
5. If you have done everything correctly you should hear the caliper motors retracting. The yellow parking brake symbol with exclamation point will now be illuminated, indicating you are now in maintenance mode.
6. Switch the ignition off.
NOTE: Mazda does not want the piston rotated when servicing the caliper, just pushed back. Rotating the piston may damage the caliper internal parts.
Exiting service mode:
1. Switch ignition ON, engine off. Note Steps 2 and 3 must be done within 5 seconds.
2. While simultaneously pressing the accelerator pedal down fully, and pressing the EPB switch and holding, switch the ignition OFF. You need to hold both the accelerator and EPB switch in this position during the next step.
3. Switch the ignition ON, while maintaining the depressed pedal and EPB switch.
4. You should hear the caliper motors performing the automatic adjustment and the yellow warning light should go out, indicating maintenance mode has ended.
5. Switch the ignition OFF.