Most worker placement games must be played in order because typically if someone takes your spot, you have no ability to contest that action. So order matter because the better spots are taken first.
But because Carson City has dueling could you just allow everyone to go at once? The only mechanic this compromises would be passing to determine order of choosing roles. But I figured you could just determine that order based on who placed the fewest cowboys to those who placed the most cowboys.
The sheriff would be an exception and would always have first choice.