Not sure how it would work with US law but in UK you would be at risk of not be insured properly and having to pay aditional premiums or even having your policy declared void.
You can't just pick the closest model to your because they don't have your's on the list, you would need to phone them up for a proper quote
if your insurance documents just say Mini, not JCW
Mini or Mini Cooper S with a JCW
tuning kit, what do expect them replace it with if it get's written off?