All L4 motors are pretty balance-sensitive above about 2.2 liters (134"), it's not an accident many engines fall between 2.0 and 2.2.
It's just not possible to balance them enough to take the shaking out (except a counter-rotating weight, etc.).
The best way to reduce this is:
1. automatic transmission to un-couple the driveline from the vibe
2. big rod ratio to reduce the side thrust (long rod, short stroke, both)
3. absolute minimum reciprocating weight (light rod and piston with short compression distance and small pin)
4. squishy motor mounts
5. high quality damper specifically for this engine