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Good track cars aren't necessarily good street cars. By modifying an SS 1LE, you are going to shift the balance that GM has established. If you make it better for the street, it'll probably be worse on the track. If you optimize for track, it's going to be worse on the street. If you find a way to make it better all around, the folks at GM will want hear your ideas.
The SS 1LE is perhaps a better track car than the ZL1. If you look at track fast lists it's not uncommon to see SS 1LEs running faster than the ZL1s. For many tracks, it really takes a great/pro driver to manage the power of the ZL1 properly.
Heat will probably be the least of your track worries. When you add significant horsepower, you need all of the suspension, aero, tires, etc. to bring the car back to a balanced track car. (Otherwise, the car will be a handful.)
In other words, adding a supercharger will almost certainly require some compromise in track capability. You'll just have to decide if that's what you want.
Good luck.
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