My personal opinion, still unbiased by the above timeline:
I think for such an action after 1850, Saxony is simply too weak.
The authoritatitve unification, as Prussia performed it, involved heavy military
actions and threats. Saxony would not have managed to.
I suppose you wanted to model acc to Prussia's example.
If, however, you are requiring a different style of unification,
based on the desire of the people, say, then you will not get
a leading role of just one state (which is not the strongest one.)
Saxony might of course claim leadership in concepts, as a
spokesperson for the crowd, but not much more.
Nevertheless, the implications might be worth analyzing.
On the other hand, if you go far back, it is easy to find a more
central role for Saxony in Germany (actually I am also doing so
in my own timeline). But I had the impression that you are asking
for a PoD after the Congress of Vienna?