we have at least two witnesses who confirm the diffculty of the defilee at Dornburg, Belliard and Dupont, they both agree about the huge problems to overcome this, the French had to double or to triple horse teams to bring the guns and waggons up.
Despite all those effort, the Prince de Ponte - Corvo was only able to be with one Division and some cavalry at 16:00 hundred at Apolda.

I will check on Hohenlohe, maybe you can be so kind to tell me where you did find it, so I can find it easier

Also I found a difference in the distances in literature, a good way will be to consult a map to track the roads and find out the distances.

Titeux and or Vachée figure out it takes about 2 hours to kick a army corps into a full move.

Rüchel needed - for example as well - 2250 meters per hour, and he did march in daylight with fresh troops, the Prince de Ponte Corvo had to march at night, the troops were exhausted -and then a very dense fog came up - along with the diffuculties of the defilé explains at least some delay.

I have to find out in what road Murat did take, it could be - that the first corps had to wait for a while to have "clear" roads, anyway road again usually were reseved for waggons and guns, so the infantry had to move at the banks of it in darkness.

I still have some fog to lift, especially about the dragoons of Sahuc.