Of course ending range anxiety isn't really possible since it´s a very relative term.
But let´s say they have come up with something to improve the range of the car.
It´s a know fact the all electric motors operate more efficiently under heavy loads. Now I´m not an expert at the engine Tesla uses but speaking from what I know, at cruise you are using about 30 hp, thats around 22.4 kW.
<snip graphs>
Now pay attention, this does not directly reflect the efficiency for the Tesla motor. Just to clear that up.
Looking at couple of graphs for VFD induction motors, shows that when cruising at around 60-65 mpH the efficiency isn't really all that good. Now the problem is basically that the engine load is simply too low. A gearbox via OTA is impossible to do within current laws of physics.
They may have figured out a way to run the engine at full power for extremely short time intervals. In my mind, this would make for an extremely unpleasant and "jerky" power delivery, but like I said, i'm not an expert at these things.
Or it could be something boring like a new navigator thingy.