Switching from full to half wave rectification
Using only a 2 phase supply, how do you switch from full wave
rectification to half wave after a specified time period?

It's probably conceptually easier if you always use a full wave rectifier and then, on the DC side, use a MOSFET to activate the brake solenoid, and, after a short while, deactivate the MOSFET for every other half cycle.
If you see the reasoning here; the &quot;control&quot; circuit is located on the DC side of the rectifier and you can more easily derive a logic supply for a timer so that after a short while of operating full-wave, you revert to half wave. It also means that you can control back-emfs more reliably compared to the situation of your control circuit being on the AC side of the rectifier.