A hydraulic control system for a machine is disclosed. The hydraulic control system may have a work tool movable to perform an excavation cycle having a plurality of segments, a motor configured to swing the work tool during the excavation cycle, and a pump configured to pressurize fluid directed to drive the motor. The hydraulic control system may also have at least one accumulator configured to selectively receive fluid discharged from the motor and to discharge fluid to the motor during the plurality of segments, and a controller configured to implement a plurality of modes of operation. Each of the plurality of modes of operation includes a different combination of segments during which the at least one accumulator receives and discharges fluid.