Same issue since 2011, tried several things that solved that vibration problems but arise again after sometime.
1- Engine Mounts
2- Auto chock sensor or throttle body
3- Loose or tight tappets
4- Leaked engine valves
5- Timing
In the beginning mine was No. 3 but that was unable to fix due to No. 4. I replaced the engine but the problem still existed which was due to No. 2 and that was solved by changing throttle body and some wiring works by electrician. After this whenever I have the issue again, I check engine mounts, I don't know if the engine mounts are not of good quality or what but they are usually worn out/ broken. This time I am thinking to change my transmission as I think there might be some issue with that, the jerk of auto shifting is quite noticeable and I think this jerks of shifting mess up the engine mounts.
I don't really like the EJ series engines, thinking of swapping engine if changing transmission doesn't solved the vibration. I have heard that Move's engine fits better without alteration in engine bay but the problem is that Move's engine is 660cc and I don't think it will be powerful enough for a bulky car like duet.