Other people have addressed several of your issues, so I'm just going to look at the claim that driving uphill empties those batteries in very little time.
As far as I can tell, the steepest drive in the United States (from the beach to the top of Mauna Kea, HI -- not entirely paved) is approximately 13800ft / 4200 m above sea level. Since the mass of a Tesla Model S is 2100 kg, this would consume 25 kWh of energy (30 kWh if you loaded it with 300 kg of people and stuff and factor in a 93% motor efficiency). The energy stored in a full Tesla battery is either 60 or 85 kWh, depending on the model. The drive from Hilo is 43 mi / 71 km (or Kona is 64 mi / 103 km), which over flat terrain would consume 15 (or 20) kWh, for a total of no more than 50 kWh. Thus, you could easily do the drive in a charged 60 kWh Model S. And, the drive back would be entirely free because you just brake all the way down -- just don't charge it at the top unless you want to burn out your brakes.
In theory, the potential energy of a Model S (+300 kg) on top of Mount Everest is 59 kWh, so I don't recommend that with the 60 kWh battery, but then I suspect you'd have issues trying to drive any car to the top of Mount Everest.