I have this issue as well on my 2013 Transit Connect. I changed the passenger engine mount and that provided a relief from the vibration for a few weeks but it came back. I also replaced the transmission mount shortly after that, but it doesn't make a big difference. I still have vibration for a while after a startup. Perhaps there's some higher-quality engine mounts which perform better, but I've decided not to invest further into it - along with the rough handling, it's more of a work vehicle, not some luxury vehicle with a smooth / vibration free ride.