Do you believe 1 City of Lumberjacks can withstand 12 Duchy's worth of armies? You're one city in one county. There are 24 counties in a duchy, each with settlements, some with similarly large cities. You're already outnumbered in your own duchy. Now multiply that by 12. Combine that with the fact that the Dukes and the King are all receiving tax money to pay for professional soldiers and equipment, while you're chopping wood.
Good luck.
Now let's say you try the diplomatic approach. Consider this- if the King himself were to award you autonomy, how many other cities would also petition for the honor? Now the King is facing a tremendous challenge of maintaining the unity of the realm. Therefore, it is only in exceptionally rare circumstances that any city would become an independent state.
On top of that, would you need the Story Points and the Influence to maintain the title? It's basically a kingdom of 1 town, trying to negotiate at the same table as the full kingdoms themselves.