Driveline slack
 

My drivetrain feels very loose when transitioning on and off throttle in gear. Is the front mount the one most responsible for keeping the engine/transaxle from torquing back and forth?

The engine has a mount and the transmission has 2 mounts. The engine mount is a problem with older cars as they age. The engine can contact the body and you get vibrations.

Local independent shop replace 3 engine mounts in 2 weeks.

Don't know if that is the problem, but it would be the first thing I would have checked.