In the process of trying to find what is causing a vibration in my engine I have tried several tests.  One was a different cylinder/piston combo. 
The second cylinder has the numbers "44500" across the base, however my other cylinder does not. no improvements were noted.  Now looking at bearings a a potential problem.

In any case, are the cylinders labeled 44500 the same as those non-labeled?

 
 

Engine mount bolts must be tight, that's always my first thought. 360A have bonded rubber mounts top rear, are they still in one piece.

Engine is torn down and looks like I may have found a possible problem... DRIVE AXLE BEARING.
More to come...

Have the crank checked for alignment/true.  

In my experience, the difference between a crank that is just barely "within spec" and one that is pretty much perfect can be felt in terms of vibration.