Perhaps instead of trying to restore Europe after the Napoleonic Wars the victorious powers decide to conquer what they can. The Prussians unite most of Germania under the Hohenzollerns, and the issue in Louisiana is resolved by giving most of the land to Germany, while the rest goes to Britain (Canada). France has to pay the US back, and the US is allowed to keep New Orleans and all territory east of the Mississippi.
Germans begin settling in the southern Louisiana territory and into Tejas from Mexico. The land is better and gets more immigration. A brief War between Mexico and Germania follows in which Mexico loses. Well you catch the drift, by the early twentieth century the Germans in Texas start wanting more homerule. The Kaiser puts a brother on the throne of Texas, but the colony remains attached to the German Empire, but eventually declares indepdence for some reason or another.