This is more /u/ErzherzogKarl 's wheelhouse than mine, but from my understanding (based on Michael V. Leggiere's Prussia-centric books), you're on pretty solid ground. The main thing I would add is that as far as I know, the Fall Campaign of 1813 was the first time Napoleon faced all three Continental powers simultaneously, and using a well coordinated strategy. In 1805, he fought the Austrians and Russians, essentially defeating them in turn at Ulm and Austerlitz. In 1806, he destroyed the Prussian army in a matter of weeks after Jena, and then crushed the Russians at Friedland in 1807. In 1809, Austria stood more or less alone on the Continent, with both Prussia and Russia in their unwilling alliance with the French.

By contrast, when operations commenced in 1813, both the Prussian and Russian field armies were in theatre together, and could not be defeated separately. This problem was exacerbated further after the summer armistice, when the Austrians joined on the side of the Coalition. Now Napoleon had to fight three large armies in the same theatre simultaneously. Furthermore, the way they were arranged (one to his north in Brandenburg, one east of him in Silesia, one to the south in Bohemia) meant that an advance against any one of them would endanger his flanks and rear. On account of the ensuing string of defeats suffered by his subordinates and Napoleon's rushing back and forth across an increasingly depleted Saxon countryside, he lost 250,000 men in combat and 50,000 to disease in about a month.

Let me know if you have any follow up questions; I think you have a good handle on what you're doing.