Thanks for the answer! I was just worried that the game might not count you being Independent if you're the leader of a pre-existing faction.
And thank you for the further information! The first point isn't an issue for me, as everything besides being the ruler of my faction (Southern Empire) has already been completed. I've got excellent relations with all of the Southern houses, my clan has reached Tier 6, has a current treasury of 2.64 million Denars, and owns 15 fiefs, and Ira being married to a Khergit means she can't inherit the Empire, so hopefully all I really need is for Rhagaea to pass on.