As someone that owns an Elise with a stock supercharger, I have to say it's not worth the effort. I'd just get a BOE Torque 200 tune and call it a day. I was at Streets of Willow with another owner with a NA 200 tune over the weekend and our straight line speeds were pretty much identical and he doesn't have the issue with heat soak. Hell, I've actually considered taking off the stock SC and going NA.
I've heard people say this before, so you are not alone in that thinking -- but this doesn't make any sense to me. 190hp vs 220hp in a 2000lb car, plus all the added torque - with the same driver in the same car in a n/a vs a supercharged car it's obvious that you would be able to pop out of the corners quicker with the supercharged one - there is no way it can't be faster. With proper ECU tune you can squeeze another 10 to 20 hp on top of that.