Passenger side lateral mount had a crack in it (visible only by using a screwdriver to twist it's rubber). Got it changed, as well as the metal plate that binds the mount to the gearbox.
Heavy dhug dhug noise at startup is gone. Vibrations are noticeably less, but these two mounts pictured here (front and rear ones) are still pretty much in the same state.
Any takers?
(btw, during this job I discovered the rubber pipe connecting MAP sensor to intake mani. cracket from two places, replaced it, and now mashallah car is running much better, also soldered some wires to get O2 sensor emulation functional for cng).