Bill

Thanks a lot - I checked Petre and used his map, the distance the Prince de Ponte Corvo had, was more than 6 miles, I would say about 16 km - a division in full daylight would need about 4 hours to march that distance, in case you have to march at night - one would be slower.
In case - as you stated the Prince de Ponte Corvo - arrived in Dornburg already at about noon, he was remarkably fast - he had exhausted soldiers, Murats cavalry in front of him, had to march at night and needed about 2 hourse to get his corps in movement (as Davout at about 06:00).

About Hohenlohe, in case I understand this correctly - it was not Hohenlohe but the detachment Holtzendorf. Please note - they did not move on the right bank of the Saale river at the 13th - this wouldn't be possible there a lot of French units moved already on this road, Murat's cavalry.
I am not aware that Holtzendorf did cross with his whole detachment the defilé at Dornburg but stayed at the left bank of the Saale.
You are of course aware that this detachment was originaly designed to cover the right flank of Braunschweigs column.

Bien que convaincu qu'une défense efficace impliquerent de rejeter les Francais au-delà de la Saale, Hohenlohe conforme à l'ordre recu. Il se contente d'envoyer un détachment sous les ordres du général Holtzendorf vers Dornburg pour assurer la sécurité di flanc droit de la principale armée prussienne.
p. 194, Stephane Béraud : La révolution militaire napoléonienne, 2 les batailles, 2013

So I cannot see that any Prussian column would use the Naumburg / Dornburg road at the 13th and therefore I cannot understand you argument that "Hohenlohe" moved faster than the Prince de Ponte-Corvo, they moved different roads, at different times and had to move different sized units.

The big problem - as it seems, that one that costs a lot of time was the defilé at Dornburg, confiremd by the Prince de Ponte-Corvo (who is accused to exagerate to cover his mistakes and disobedience - where none existed in my view) - backed up by Belliard (correspondance de Murat) and Dupont (Titeux).

Petre : Looking from the Saale up the valley leading from Dornburg to the plateau, there seem few difficulties, certainly none such as Soult had in the Rauthal.
P. 172, Petre : Napoleon's Conquest of Prussia 1806, reprint London 1972

So Petre is looking from Apolda or Jena or whatever into direction of Dornburg, he ignores the defilé of Dornburg and the crossing of the Saale on a single narrow bridge.
Clearly he describes the terrain of the left bank and not the right bank of the Saale.
And I cannot agree that Soult faced more difficulties in the Rauthal which I walked about 15 years ago during a re-enactment tracing Soults approach march - than the Prince de Ponte-Corvo at Dornburg - I am not aware that Soult had to double or triple his horse teams to overcome obstacles.