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2005 E350 extended body, Ford 5.4 reman'd engine installed about 15K miles ago. Since day one I've noticed a vibration of sorts I thought was related to the engine itself. I don't recall this vibration being present with the failing original engine (143K miles) so it might have been present, I might have paid more attention to it when the new engine was first started (looking for issues before putting the van on the road. (There was an issue with the Bank 1 passenger side head replaced under Ford warranty due excessive valve train noise---vibration was present before and after that replacement.)
At idle you can feel a small vibration two of my other E-Series do not have---both of those completely original to the chassis. Even when in Drive they're smooth. With the '05 during acceleration you can feel what seems to be a super low grade misfire, as though the engine is struggling just a bit---when at a steady freeway speed the vibration seems to smooth out. A cylinder contribution test shows no issues in the ignition system, all working perfectly.
When shutting down there is a minor "shudder" similar to the 80's GM's that would "diesel" when the carburetor wasn't adjusted correctly. This is also very minor but become more noticeable in the past few months. Soooooo......
What would symptoms of a failing motor mount be, how would I visually inspect them and how can they be changed if necessary?