My sons has a Tesla S and I ask him if something happened that the car took a mind of its own went to accelerating and wouldn't stop, how do you shut it off to avoid a collision? He wasn't sure. We worked together and found one thing he could do is put it in neutral. There is no way to our knowledge to shut it off while driving. If there is other alternatives please reply. Every owner should be prepared for an emergency such as this. Randy
... and OP has left the building.
Sorry for reviving this discussion, but the OP has touched my concerns quite close. After reading throughout the whole discussion and a little tech research on braking my worries haven't been eliviated a bit. They don't apply exclusively to EV/Tesla, but to classic ICE cars as well, -but less so.
Imagine yourself going downhill after fully charging at your at home. In case of an electrical (or other) failure your main brakes might stop working partially (no servo boost) or completely (blown fuse, software error, leaking hydraulic system etc.) and you would get into such a "runaway condition".
In an ICE you always have mechanical motor braking available to get the car to slow down, even on steeper slopes when in first gear. This is comparable to regen-braking on an EV, but as we all know, this isn't always available (=fully charged or cold battery) and would be a very probable situation when starting your downhill journey.
What options do you have now while the car keeps accelerating? As mechanical handbrakes are more and more replaced by electronic parking brakes in all cars I would keep pressing the "Parking brake button" as instructed, but it works only if there is electricity present to run the actuators at the rear brakes (a known disadvantage according to wikipedia). Sure, this last resort applies to ICE cars with electronic parking brakes just as well, but here I still have the motor braking available all the time as a backup to slow me down.
Maybe the OP exaggerated the hypothesis a bit ("meltdown") but keep in mind that we have a car quite close to formula 1 specs in driving dynamics on one hand and look at their brakes glowing hot when these cars go through corners on the other hand. Now guess how long these brakes would work when trying to slow down a "runaway of 600 horses at constant full throttle" and 2 tons of weight. I don't know, but would have loved to have read some technical reassurance instead of suggestions like "Hit. the. brakes." or similar.
Disclaimer: Flawless MS90D from 2017, private owner planning to keep it forever, no direct or indirect involvement in car business, about 12.000 kilometers in Central Europe, partially in a rented Tesla (prior to ownership), technically inclined and long time EV observer convinced about the future of EV cars in general and mine especially.