Is it possible to do "runtime" routing/switching of current paths?
You could connect one leg of all the motors to one half of the bridge and switch the other leg using cheaper (than the H-bridge PCB) relays.

It would be a huge pain to use MOSFETs to switch that in a custom solution, and typically you would just dedicate one H-bridge per motor.

With dedicated H-bridges, you can use your knowledge of digital multiplexing to control them easily.