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Post #9 schematic presumes a bipolar buck converter (5) which isn't practical at all.

Practical solution is an unipolar (usually positive voltage) buck converter followed by a commutator circuit, either mechanical DPDT relays or MOSFET H-bridge. It's simply a question of minimizing circuit cost, number of components etc.

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Simplified schematic of buck converter with commutator:

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Component count could can be further reduced with H-bridge buck converter, but in terms of noise filtering and control signal generation, the first schematic is often preferred.

The buck converter (M1, M2, L1 and C1 with associated control circuit) can be an off-the shelf module.

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