Great idea, just a word of caution. The 10-30 outlet is obsolete and cannot be used for new installations, you must now use the 14-30 (hot-hot-neutral-Ground). The 10-30 can still be purhased and used to replace and existing 10-30 outlet. I believe as long as you are only tuning the outlet around to face the garage you will be within code, but if you have to add wiring then I believe this will be considered a new install and a 14-30 will be required, by code.
I suggest you consider running a new circuit from the breaker to the garage and terminate at a Tesla Wall Connector.