Use of a slow-motion camera to diagnose a vibration is a killer technique!
By the nature of a reciprocating engine using short (actually, finite!) connecting rods it is impossible to perfectly balance the moving parts just by altering those at crankshaft speed. The F=MA for the rods and pistons moving down is not actually exerting force equal and opposite to those going up throughout the entire rotation.
Another way to say the same thing: The forces exerted by the various moving masses as they accelerate/decelerate are not sine waves at crank rotation frequency: If they were they could be fiddled to cancel out. They're distorted so that the best possible cancellation still leaves 'bumps' of force at multiples of crank rpm.
The unbalanced force is zero at crank rpm but non-zero at even harmonics 2, 4 x crank rpm. This can be cancelled (thus giving you a much smoother running engine) by installing shafts with properly chosen counterweights that rotate at 2, 4 x crank rpm and that are properly timed to cancel the unbalanced force from the rods and pistons.
I think this is a remarkably ugly scheme but it works: I've got cars with very similar Mitsubishi engines (I4's, same year but different displacement/model) both with and without balance shafts and there is a dramatic difference in the smoothness of those engines. The arrangement on the (balance shaft) 4g64 engine is quite unlike that on your engine but it is easy to time the 2x shaft 180 out so it doubles rather than cancels the engine vibration. Mechanics do this rather frequently and I've actually driven a car that was mistimed -- it was bad.
The good thing about the Mitsubishi scheme is you can check for this mistake quite easily -- put the engine at TDC on #1, take out a plug on the block, stick in a screwdriver, and if it goes in 60 mm that shaft is correctly timed. If it goes in much less it's wrong and you must do the timing belt remove/replace operation and this time follow the directions for correctly timing that shaft.
I just did that process in order to replace the oil pump on one of my cars ... 4-6 hours work if all goes well. But checking takes 5 minutes and I could do it in a parking lot with just 12 and 22 mm sockets and screwdriver.
I don't know if there's an easy way to check shaft timing on your engine -- a forum for that car or engine would be able to tell you. If it's wrong you have to remove the pan and the timing shaft assembly to fix it.
A good mechanic would deal with this pretty quickly if there isn't anything in the way of getting the pan off -- like a transfer case for 4WD for example. How you find that mechanic I've no idea: The reason I do almost all my own work is I couldn't find one in this semi-rural area.
I make plenty of mistakes but only really stupid ones -- not the ones you can avoid by reading the directions.
