Great idea -- I'd really appreciate it if you could update us with what you find out. I'm with AAA (for now), and they're great if/when you have to file a claim, but, ouch. Hard to rationalize staying with them.
I contacted two Tesla certified shops in Atlanta (closest to me) and their favorites are:
1st shop: Esurance, Liberty Mutual, Geico, ALFA, Chubb, Hagerty, Pure, and Protective insurance
2nd shop: Country Financial, Georgia Farm Bureau, Travelers, USAA
The 1st one said Esurance is very easy to work with and rarely gives any trouble with repairs so it seems I am good.