For using the 2. nd transformer tap, there are two more simple solutions:
1. Use a robust transistor (e.g. like 3N3055) that can stand a high base current. At low output voltages this transistor works as an emitter follower with the low rail at the collector. At higher output voltages the transistor can not work as an emitter follower, but just the base emitter diode is active, so the normal driving stage does all the work. For protection a diode is needed in series with the collector.
2. Use a circuit like a class H audio amplifier: Similar to you circuit, but using a N_MOSFET as source follower or an NPN as a emitter follower, with a constant voltage at the base of gate. So no need for U5. Often just something like 5 V used for the supply of the OPs is about right.
The downside of both methods is that the power dissipation will shift between the two output stages, as there is not hard switching, but linear operation.