A larger battery will not give any more time on the track. The limiting factor for track time is overheating of the PEM and motor, and a larger battery would quite possibly add more overheating - because the battery will be able to supply more power, which means the PEM and motor will be working harder. And between sessions you want to plug in the car immediately to help cool the battery anyway.
Anyone who likes to push the Roadster in terms of performance would prefer a lighter car, as adding lightness is simply the best way to make a car better across the board, which would make it a better track car by far. And a lighter car would allow for more track time since less weight means less power to push that weight which means less strain on the PEM and motor. Also, lighter cars are more efficient anyway so you would have a natural increase in range just from that.
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I beat ideal miles on the way to San Diego from Orange County, on the freeway the whole time, on a slightly hilly drive, not holding up traffic (kept it around 65mph mostly), not really drafting (though I took opportunities here and there). I was just easy on the accelerator and never used the brakes (not even regen, usually, as regen is less efficient than using steady power), and I think kept the AC off.
I really don't see how people have trouble hitting ideal miles if they need to.
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