Yah, welcome to a lightened flywheel.
Check your wheel pressures, put them at the recommended 36f/32R, it will help a little.
It rattles because with a lightened flywheel you have a lot less inertia to keep everything meshed in the tranny. It seems like some of it is helped by replacing the various bushings which generally tightening up drivetrain.
The tranny/engine mounts, Rear Diff bushings, the tranny crossmember bushings, all seem to help some. Not to mention your entire drivetrain will feel better.