It's hard for me to think like a murderer; however, there is no way that I believe a random killer would want to take a chance and stick around long enough to shower in this home. His thought would be to get away from the crime scene as soon as possible.
If it were random (which I don't think that it was), the killer might grab some of Jason's clothes--assuming that he would know where things were kept and assuming that they would fit--and change into them. However, he would not stay and shower.
It was no random murderer who showered there. It was no random murderer who changed into perfect fitting clothes of the husband. I don't believe it; and neither do the police. I'm not an idiot; and I know that they aren't idiots, either.
Jason knows that he did it. He also knows that it is up to the police to find enough evidence to arrest him. He is just sitting tight, not saying a thing, hoping that they won't find enough evidence.
I can't wait until Jason finally decides to press for the insurance money. He'll have to sue for it, IMO. It will be interesting to see what transpires, then. I think, at this point, he is afraid to ask for it and won't press for it...not because it wasn't part of the motive, but because he doesn't want to rock the boat, at this point.