The vibration description appears to have conflicts when you mention being stationary, gear engagement or not, driving at constant speed, and running down through the gears at fixed road speed.
There isn't common rpm for any part when you have an idling engine with output side to the drive train not in motion, then variable rpm from the engine and input side of the gearbox, including torque converter at different rpm as you use the gears. The constant vibration in motion at 100km/h would still look to be 'post gearbox' for picking up rotational induced vibrations. Engine induced vibrations (including engine ancillaries and torque converter) should typically change with rpm. Hard to picture the same harmonic vibrations from an engine across its rev range, from and including idle.
It is the gear selection position changes which intrigue me most, as if it is torque converter related, but how and why in such different situations and the rpm changes?
Need to think about this a bit more, as your description doesn't fit any usual model I've ever used for fault finding.