generally lose or depleted or whatever you like to call them engine mounts cause this symptom, but could be another issue due to previous repairs but that is highly unlikely as you say it runs smoothly at high speed, let me explain in common physics (sort of) at high speed and rpm the body of the car cant vibrate at the high frequency vibrations of the engine so it stops vibrating , but it vibrates at low vibrating speeds because it can cope and vibrate at same rate, these can be replaced at relatively low price around 2k, so good luck, experts can guide the rest