In looking at the manual that is accessible from the information linked in the question, I can see that the motor is definitely a permanent-split-capacitor motor. Reducing the capacitor value will likely reduce the speed. You can never tell in advance how well any method of speed control will work with a single phase motor. Ceiling fans are generally designed for speed reduction and there is a substantial history of success by people using methods other than those sold with the fan. There is a good possibility that the speed your fan by reducing the capacitor value will work fine. Try a capacitor value that is less than the original but as close as possible to the value of the original capacitor. The speed and the motor current should be less. There should be no problem with the fan overheating unless the motor current is not less with the new capacitor or the speed is so slow that the fan does not move enough air to cool itself.
Turning the motor on and off with a micro controller is not a good idea. The motor will draw a higher than normal current each time it is re-started and probably overheat. If the on/off time is for milliseconds rather than seconds, it will be like a dimmer.
The curves below show the effect of changing capacitor values. You can see that the amount of speed reduction is limited and the shape of the fan load curve helps to make speed reduction possible. The reduced load torque at lower speeds helps to keep the motor from overheating. Overheating can be somewhat predicted by measured current vs. the motor's rated current. Measuring the surface temperature of the motor is also somewhat useful. Motor shaft temperature could give some indication of rotor temperature. High motor slip means higher losses in the rotor.
Note that the drawing shows a motor that has a high slip with the highest curve. A high slip motor provides a wider range of speed control, but a low slip motor is more efficient. If a motor is designed for high efficiency, it may not work well with capacitor value change and voltage reduction speed reduction methods.
Note also that the fan load curve is pretty close to the motor torque curve at low speeds. Some motors have a dip in the torque curve in that area that would allow the load curve to cross the motor torque curve at more than one speed. That would allow the motor to run at a stable low-speed point. The load may be low enough so that the motor does not overheat, but the fan will not be providing much cooling air. Since most of the losses are in the rotor, it may be difficult to determine if it is too hot. The bearings may be most vulnerable of excess rotor temperature.