If I remember correctly, Chief Hanlon's betrayal was more about getting the army, specifically the Rangers, out of the Mojave. He wanted them out because he disapproved of the whole war and how much the NCR was exhausting (especially in terms of lives) for a foreign land and ungrateful people. So he falsified reports and messed with logistics (like sending outposts asking for water ammunition instead) to make the whole war seem worse than it is in order to gain support for a military withdrawal. It was never about him wanting to form a new republic.