It appears like an important reason behind Bavaria leaving Napoleon in 1813 was ambitions to play an important role in post war Germany.
So, what if, Napoleon actually is defeated (killed or taken prisoner) at Hanau in late October 1813 by the Bavarian-Austrian Army under Wrede he met there? (NB: Hanau is splendid to wargame, has a lot of interesting options - and colourful troops).
By the late Napoleonic wars Bavaria had a relatively very strong economy, being able to on her own fielding 40.000 well-equipped men in 1813 and 55.000 in 1815, and apparently also had their own bid for "the German spirit" rivalling that of Prussia.
With the Napleonic wars ending in late 1813 by Bavarian-Austrian action, the British and Prussian roles will also be smaller (sans 1814 and Waterloo) and the Prussians will be unlikely to gain all the rich territories she did in OTL 1815.
With that, and the Bavarians feeling themselves masters of Germany (and perhaps later the Universe
), a Prussian led unification of Germany is very unlikely.
The Bavarians and Austrians will still have some serious unsettled business, but no mater what the outcome is, the result is likley to be a relatively loose German confederation, with or without Prussia and a number of north German protestant states. If the Prussians and/or north Germans feel too pressed, the religious factor may become important (Protestants vs. Catholics) making a coherrent unified Germany even more impossible.
Regards
Steffen Redbeard