Cottonwood
Roadster#433, Model S#S37
You should be able to wire a 30 amp dryer receptacle and corresponding breaker to this. You might find that this is enough. I would charge at 25/24 amps with that setup.
I agree completely! See American wire gauge - Wikipedia. Even at the lowest insulation temperature, you can do 30 Amps with #10 copper. On top of that you have all 4 wires (two hots, neutral, and ground). Put in a NEMA 14-30R (Receptacle), change the breakers to 30 Amps (rating for wire and receptacle).
With this set up, when you get the 14-30 adapter from Tesla, the Mobile Connector will automatically set the correct current of 24 Amps, and you don't have any cheater cords. The 14-30 has enough stiffness that the Mobile Connecter will dangle from it nicely, and you have a good, clean, current-code-compliant installation.
Good Luck!