That has all the signs not of an attempted carjack, but an attempted kidnap. I think YOU were the target, not your car. His conversation on the telephone confirms it for me. If you'd got out, he'd probably have tried to get you into HIS car. If he'd wanted the car he'd have rushed you with his gun out from jump.
A woman alone is often a target for this kind of thing. It is one of the reasons I carry. I have about a quarter mile walk from the courthouse to my car every day, alone. Anyone who wanted to try something would have ample time and opportunity to do so. A disarmed woman is a nother term for "victim" in our criminal society. I'd bet that he knew you were armed after what you said to him about backing off the car before you had to protect yourself-that and the police inbound to your location's why he ran.