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.

Resurrecting this thread, because I have the same issue, persistent even after replacing all three mounts. We are looking at a 2000 Boxster S 6-speed manual trans car.
It goes like this: when babying the car, it is barely noticeable. when accelerating even just moderately it starts vibrating ( under load...when accelerating) most notable in first three gears. Abrupt throttle off, and back on produces a very prominent "clunk" type sound. Not really loud, but very obviously something taking up slack in both directions.
The car does not steer when this happens, and it does not seem to be coming from the axles or clutch. It's more like right under/behind the driver seat.
The engine mount was replaced very recently, together with the rubberized spacers to the left and right of the mount. Both trans mounts were done at the same time. CV axles also fresh. The entire rear suspension is brane new and has been pro- aligned. Tires are brand new. Brakes also. Not that I suspect tires and brakes to cause this thump, but just for clarification.
Weird one, this one....any thoughts ?