D’rabanan in a makom mitzva is mutar on shabbos
That is absolutely not true. Rachmana litzlan if anyone were to follow that advice! If fulfilling a mitzvah d’oraisa requires violating an issur derabanan you may NOT fulfill the mitzvah. Shev ve’al ta’aseh.
Double derabonons, called shvus dshvus, like asking a goy to do a derabonon, is mutar in most cases for a mitzvah.
This is closer, but still not correct. A double derabanan is mutar if and only if it is absolutely impossible to fulfill the mitzvah at all without it. If there is some way to keep both the mitzvah and the double-derabanan prohibition, even if the mitzvah’s fulfillment will only be minimal, without the usual hiddurim, one may not violate the prohibition.
Therefore even if driving a Tesla is mid’rabanan it would still be forbidden even if that means not davening at all, let alone merely not doing so in shul. Only if it’s a double derabanan, and there’s a mitzvah that can’t be fulfilled any other way, would it be mutar.