he got lost.
and the napoleon did in fact use divide and conquer as you have said and i never contended against. this is why he sent a detachment to keep on the prussians heels after he defeated them after isolating them from the allied contingent.
and evidence in my opinion that he got lost is that the prussians regrouped. if he had remained hard on their heels this would not have happened.
note lost being he did not follow on the prussians as had been planned and ended up off track to the south of them following what he thought was the prussian main body.
grouchy did in fact finally realize his mistake but by then the prussians had bypassed him.
and just hours before the battle ended is a shocker. also i said that the prussians got within a few miles before they were spotted which would still coincide with your record of the battle.