I do believe that a MODERN sound proofing material under the bonnet will make a useful difference. Some of the more traditional materials merely trapped water and caused rust. Some of the stuff that looks like aluminised bubble-wrap is both a sound and heat insulator, and should achieve useful results if the bulkhead is properly covered, which means having the subframe out.
I also noted many years ago that a standard (in those days) traditional sound insulation kit had 4 triangular pieces which were glued to the bonnet, between the stiffners, and those definitely do damp certain resonances, and make a slight, but worthwhile, difference.
But making the Mini quieter needs a comprehensive approach, giving attention to damping panel resonances, which means replacing the bitumen pads (possibly with something similar but better) that are usually removed for floor repairs etc.