Like I said above, IFTTT could be option, assuming you have cell coverage (my office garage doesn't have ).
IFTTT would detect proximity to the car and unlock the door when you're <10 feet from the car. We'd be talking about second or two response at max, much faster than typical BT pairing. Although if active, BT could ping you further out, typical range is fairly good. But that would drain your battery if it pings actively all the time. IFTTT could do push style to the car data modem so it'd work perfect.
I think there's already some IFTTT services for MS/MX, so they could expand those to M3 also.
Anytime the vehicle is sleeping it will not have connectivity of any kind (Bluetooth, LTE).