I feel very strongly that JonBenet's killer was incapable of mercy.

My best guess is the following or a similar sequence, based on inference and what seem to be the facts known:
-that JonBenet regained consciousness when the garotte was slightly loosened once again,
-she screamed (hello Melanie) with all her might and the pent-up air in her lungs,
-the killer struck her hard on the head in a panic to silence her,
-the killer then quickly pulled the garotte very, very tight,
-then he tossed her body down in the windowless room, folding the white blanket over her, but incompletely,
-he closed the door and latched it,
-he carried the baseball bat with him up the stairs from the basement to attack or kill other family members in case the scream was heard by someone in the house,
-ran out the door on the North side,
-then possibly paused for an instant to see if any lights came on in the house or neighboring houses,
-then tossed the metal bat aside, causing the metal-on-concrete sound heard by Luther Stanton,
-then ...