I agree with all of that.
I love all of your posts
But - the only reason I think that he would have actually called the mother, if he were the serial killer, was if he got really paranoid thinking that someone saw her go into his house.
If he were the SK, then that is when he would have really gotten rid of her body somewhere, possibly in the ocean, so that he could be sure that no one ever found her. Then it would have just been his word against the drivers. And who would believe a prostitute driver over an upstanding local doctor?
Like I said, I don't believe that to be the case, I'm just giving a reason as why he could have used his real name when calling the mother. But still, not likely.