I think the police are interviewing quite a few people. I also believe they are finding out a lot about this suspect. They and the DA know the defense is going to be temporary insanity, so at least two things they likely will want to establish are suspect's character and evidence of premeditation. They need time to flesh out his personal history and get all their ducks in a row. Even if the jury doesn't buy the insanity claim, if defense can convince them this crime resulted from a moment of panic or rage, he won't get the death penalty, not without the necessary elements. In fact, he won't even serve a life sentence.
In a sense, people like that are insane, or mentally ill. However, he was able to work, at a psychiatric hospital no less. They will find a pattern if they look closely enough. They need a couple of highly trained forensic psychiatrists to interview people along with LE. They would be looking for a pattern that the cops just might miss.
Oh they'll go for the temporary insanity plea. I believe he deliberately pulled that stunt at the motel. He knows all the signs that indicate true mental breakdown/illness from his job. Law enforcement's job is to go through MH's life with a fine toothed comb. Find his grade school teachers and neighborhood friends. Okay maybe that is a little expensive and extreme, but I for one wonder when this started. If as the families say, he was just an average normal person, then what happened and when?
The Church and its members need to cooperate fully with this investigation. He was gone for 2 years on a mission. Somebody who was with him had to have seen or heard something. You just don't wake up one morning and turn into a sociopathic liar.
Yes I do believe him to be guilty of murder, because of his lies. You lie like that, you're capable of anything.