Running furnace fan as cooling
The common relatively (30 years old or newer)newer furnace have blowers with multi speed taps on the motor. If it is a variable speed furnace it has dip switches. Typically the higher speed is for cooling and the lower speed is for heating. Most furnaces go to the high speed for fan only operation, yours apparently goes to a lower speed. Without knowing the model number it is difficult to tell you exactly how to wire it. It may be as simple as changing the speed taps on your blower or as complicated as hooking an extra wire to the Y terminals of the circuit board and thermostat and tricking the furnace into thinking it is cooling.