Welcome from New Zealand.
If your Z3 has a manual transmission, I would recommend getting poly sub-frame bushings fitted. Leave the diff bushing rubber. The higher powered Z3's have a habit of tearing our the boot/trunk welds and cross member that holds the diff up and the poly sub-frame bushings are considered a prudent risk reduction.
Do a search on the sub-frame failure and the "Randy Forbes" repair. You will see a lot of Z3M cars with the damage. Most of these are USA based and have the S52 engine and manual transmission. Your 3.0L engine makes more torque (its torque that breaks things) than the S52 and dropping the clutch and other hard driving seems to be the cause of excessive force on the cross member and welds.
If you have an automatic transmission, then its a suggestion to get them fitted. My 3.0 L Z3 is automatic and the poly sub-frame bushings are fitted.
Regards
Murray