just get a new shell for the mini, you can still get them and bolt the thing on, nothing wrong with it then as the chassis is essentially the same.
in respect to an rs, it's mainly a base shell with other bits stuck on, except for transmission differences in some.
the value is in the title not the mechanics really, odd really, Ford for instance put some bits together as a package and call it an RS, man in a shed gets the same parts and does exactly the same job and somehow is worth less. it's all about the title not the product.
it is illegal to do as suggested though in the OP, like for like titled shells shouldn't cause much disturbance in the force though.

i had to take my xr2 to a vic test once over, i stamped a blank vin plate with the same details as this became significantly damaged in an impact and had to cut out and weld back in the floor plate, they didn't bat an eyelid. i suppose they could see panels were replaced on the front and footwells so put two and two together. would have been easy to put a ringer together though.