Firming the
suspension up makes things worse, firming the
body up makes it better.
Yes, bracing the body will help to prevent twist and that kills rattles. I run a late R53 Cooper S with 4 substantial additional braces and, even with 22,000 miles, it's almost completely rattle and squeak free!
The only problem is that the JCW item is little more than cosmetic (it's far too flimsy) and is very unlikely to achieve anything (though it's
very shiny when you open the bonnet!). I'm not yet aware of an aftermarket version for the R56 that actually works. Save your money for the moment and wait for the aftermarket to make a real one!
Tigger.
PS: This is how substantial a brace needs to be to have any affect: