Just a few bits and pieces here...
The grand jury term had just begun at the time of the crime. IIRC, it was mentioned that the prosecutors want to give themselves time to do more investigation. Also, since it is a new grand jury, they are inexperienced. It's more than likely that the prosecution wanted the grand jury to have more experience under its belt before presenting such a major case.
JRH put that little boy down on the boiling pavement. It was rough, it was hot. There was an area with the trees he was thrashing at with grass. It would have placed the child in a better environment to be resuscitated. That area was only steps away.
IMHO, LE's biggest clue that there was a problem, aside from the bizarre behavior at the scene, was the fact that JRH's original timeline had a glaring omission. He did not mention his that he went out to lunch with friends at Publix, went to Home Depot to buy light bulbs and put them in his front seat. By leaving out all of this information, he put a spotlight on it. An innocent person would have included this hunk of the day in answer to the questions about what he did that day because it had no significance for him.
Yet, he went into great detail about his pleasant morning with Cooper from the time they got up, watched cartoons, got in the car, went to eat breakfast, put Cooper back in the car and make sure he was fastened in tightly for his own protection. The embellishment of the kisses given and returned was meant to strike the cords of LE's heart as to what a "good" father he was.