[keiser]

Motor mounts?

 

[keiser]

My experience is with a 2005 V-6.
The liquid filled mount on the passenger side leaks and causes shaking similar to what you describe.
Also noise but that built up gradually so I could only appreciate the silence with a new mount.
A test is to have someone rev the engine in park while you observe the engine.
If it tilts appreciably when revved, it points to the mount.
There are other tests for the V-6 mount but replacement was cheap enough and easier than exhaustive testing.

Here's a YouTube testing a I4:

 

[keiser]

There are 3 mounts.
My experience replacing the right front mount fixed the issue.
But maybe you need to change the transmission mount?
Perhaps slightly jack up the engine with a 2 X 8 under the oil pan and see if the rough idle changes or disappears.
A simple experiment.

 

[keiser]

There are actually 3 or possibly 4 mounts.
So you've changed the most common failure [passenger side] but there are still more that could be the issue, as unlikely as it may be.
No need to keep throwing on new parts but do the quick jack test - be sure to use a board - and see if anything changes when slightly elevated.