PROBLEM SOLVED: Replaced the Dogbone and Transmission Mounts
No more Vibration!
Like I originally posted, I replaced the motor mount with a factory mount from the dealer and it helped, but I was still getting weird vibrations periodically.
Finally, I replaced the dogbone and transmission mounts and my ZTW feels new!
Very solid, quiet, with little vibration.
I guess it's best to replace the three mounts at the same time.