Maybe SP was told not to make it look like a "hit" because that would point to BB because of their past history and because they always look at the husband first. Seems like a lot of trouble to go to when they could have killed her in the parking lot. If perp. got into car no doubt Missy's blood was left somewhere unless they completely stripped off which I think is unlikely because they would have wanted to get out of there. This person IMHO staged the murder to look as if a psycho did it!!
I said in beginning if I was going to do it, I would not use a hammer. I'd use a .22 revolver. No shell casings left behind. First 2 shots .22 short hollowpoints. Then the 3rd and possibly 4th, .22 long rifle hollowpoints. A .22 in a closed building that is fairly well isolated, before 0500 on a rainy morning isn't likely to be heard. Even someone in the parking lot would likely have their windows rolled up, radio on, heater/defroster on, engine running and wouldn't notice or discern a single .22 LR shot. So why a hammer or whatever it was they used? It was personal? (That would seem to make hit less likely.) That takes a bold, confident person to plan a murder then do it up close and personal.
Your theory that it was staged may be why a gun wasn't used, but the instrument that the killer was carrying.