"...savagely strangulate her injured daugher..."
Even if she thought she was dead...and not 'injured'?
Nope, this is a set of experienced and loving parents, not some addlepated crackheads. They would have known how to check for a pulse and called an ambulance. They are not panicky people.
Autopsy and other reports all say the would to the head was a massive blow and gash (yes this could be caused by a bat) HOWEVER:
There is no blodd spattering or other forensic evidence of a savge blow/beating done in Jonbenet's room.
The autopsy said the blow to the head happened at or near death (IE her heart was not pumping blood) and that it did not bleed profusely. A blow with a bat to a live person would have caused massive bleeding,causing a large amount of blood and splattering in the room. A closed wound would have caused a massive hematoma at the impact point as the heart would have been sending blood to the injured area until it stopped.
There is no hematoma at the blow area per the autoopsy report, no large amount of blood in her room, no splattering in her room, no blood trail from the room to the basement, no pooling at her body --- ergo the blow did not come elsewhere in the house, at least not while she was still alive.