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The Tesla needs a secret weapon. Some sort of "nitrous/boost" like button that dumps full and direct power to the motors.
How about a transmission of some sort to keep it out of the back EMF?
Want to see 3,000 amps pulled from a single battery?
Jump this video up to 1:06:24 to see it:
EVTV Friday Show - July 11, 2014 - YouTube
The first battery tested pulls about 1,000; it's the second one that does the 3k.
I don't think back-EMF is the limiting factor with the P85D. I think it's the power output of the battery. The 85kWh pack can put out some serious power, but not for more than a few seconds. At that point it has to back off to protect the battery.
I don't have any technical info to back that up, but that's my hunch.