Some of it is just the nature of the beast (small motor with automatic transmission lugging down at low rpm), along with not having much rubber in the engine mounts to dampen the vibration.
Those rubber "legs" in the mount are there to help lessen vibration transfer but they can tear / break over time and when they do it sometimes lets the engine move around enough on acceleration to take the CV joints past a safe angle, then they fail too.
This was the case on our old Caravan 3.3l. It got bad enough we were replacing axles and mounts every year, until I was able to find an aftermarket mount filled solid with 60 durometer urethane (no legs). A little more vibration than stock overall, but can't tear so no more trashed axles. In later years, Chrysler started making the mounts larger with more rubber which helped.
The Evo joints are solid so no legs to tear and they'll last longer, but may transfer more vibration because of it.
As a hack, some people would take Window Weld or something similar to fill in the gaps on stock mounts to try to make it more solid.