In one aspect, a system for controlling the torsional output of a hydrostatic transmission of a work vehicle may include pilot-operated first and second valves. The first valve configured to be actuated to a closed position to occlude fluid flow through a first fluid conduit when a pressure within such conduit at a location downstream of the first valve drops below a first threshold. Moreover, the second valve configured to be actuated to a closed position to occlude fluid flow when a pressure within the second fluid conduit at a location downstream of the second valve drops below a second threshold. As such, when one of the first or second valves is actuated to the closed position, an increased flow of fluid is delivered through the other of the first valve or the second valve to increase a torsional output of an associated hydraulic motor.