Thinking about this case...
What if LE released information from their 'solid timeline', such as when MT went jogging, or that MT returned to the house after jogging, slept and left the house in the morning to go to pick up the car at her mother's house?
If you were provided any of that information in whatever combination that makes sense what would you do then? What could you sleuth from that point that you couldn't sleuth now?
Let's say, you now know MT returned from her jog, did some homework, ate dinner, slept, woke up at 6 am, showered, dressed, ate breakfast, placed the dogs in the basement then left the house to go to her mother's house to pick up the car.
Now what? What do you sleuth?