I don't think there is something like winning independence. After Fortress Siege you have 1 hour to choose between Castles your fortress might belong to. You can make this decision talking to NPCs which are inside the fortress for 1 hour. In our example it was Dion and Gludio. If you dont decide which castle you want to be contracted to, then your fortress becomes independent.
Another way of getting independence of your fortress after taking contract with a castle is not paying the taxes, which are around 25k/6hours. Can you, please, look into it once again and correct me if I'm wrong. Thanks :))