Once upon a time, one of my grandfathers was a sheriff. So naturally, I asked what he thought of this whole situation, since he'd dealt with some high profile murders. His opinion is that JP definitely killed her, and that his father knows and possibly helped.
As for what WVCPD is doing...they cannot and will not tell everything. They wouldn't call in BLM resources, their forensics resources, etc if they didn't have something concrete to tell them what they have.
As for the changing stories...that just seems logical. They let out a big piece, get the attention of their suspect, and then continue along with the "no comment" line. It's brilliant, actually, because the reaction has already been provoked.
This isn't a "well we thought there was something" it is a "we know there is something." These resources are costly, especially when your major case lieutenant and police chief are in Delta instead of their jurisdiction. Also, forensics working on this case instead of countless others.
There is something big, and we're going to find out in time. But we have to be patient. These people know exactly what they're doing.