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If you want better street and track performance then get Michelin PS4s.
275/245 set up adds 3-4lbs per wheel of unsprung weight. This diminishes handling and acceleration.
The stock 245/215 rubber was chosen in part to complement the i8's fuel efficiency / CO2 mission. Many of us prefer a minimal cost in fuel to enhanced performance.
The i8 does not have a powerful engine driving the rear wheels; traction during acceleration is not much of an issue. Power-induced oversteer is not a challenge for the 245s. The relatively skinny 215s on the front, however, are a bit of an Achille's heel for cornering. The car 'pushes' (understeers) at its limits. But unsprung weight is a true enemy of handling, so simply slapping on bigger wider tires involves compromises. There also are issues with the handling software; algorithms are based on stock tires. This is complex - but there is a fair bit of flexibility/adaptability in the system, so small changes do not present problems.
Ideal solutions require extensive comparison tests of the sort that Tire Rack does.
My best guess: If you have $$$ to burn, get superlight rims -- BBS FI-R. Michelin PS4 265 235.
Mixing new tires w used ones is problematic. That said, the $ saving choice is to get two new tires and use the old 245s, either keeping them in back and putting new 245s up front for square set up; or moving old 245s to front and putting 275s on rear. The only real gain here is appearance, if wider tires appeal to you. Your track time would likely be slower. Street feel and steering sluggish.
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