A transmission system is disclosed as having a transmission configured to receive torque output from a power source and to drive a traction device, and an input device. The transmission system may also have a control module configured to reference a signal from the input device with a map to determine a corresponding speed of the power source, and to determine a margin between an actual and a maximum available torque output of the power source at a current speed. The control module may also be configured to determine a delay time threshold based on the margin, to selectively adjust a speed of the power source mapped to the maximum displaced position of the operator input device based on the margin, and to selectively adjust fueling of the power source at a current displacement position of the operator input device and operation of the transmission based on the signal and the map.