I think we need to decide on a solid list of who the Princesses of Heart are for KH1.
The reason I don't really want us to just, increase the number of Royal Authorities, is because ultimately each Royal Authority is supposed to be bound to a Princess of Heart. Each Princess of Heart is meant to be tied to one of the Seven Deadly Sins.
If we just say instead 'now there's thirteen Royal Authorities', then now we just kinda randomly have 6 extra of them for... no particular reason other than because we think there are characters who would fit the bill of hosts for it. The Royal Authority is not really a power that grants abilities or anything. It is itself, a power that can be granted to a Princess of Light, allowing them to aid in the opening of Kingdom Hearts. The full method is:
"Seven Princesses of Light, Purged of Sin, and Granted Royal Authority, Will Empower a Grand Magus to Shatter the Seals, and Open the Path to Kingdom Hearts"
So each Princess of Light needs to defeat the sin they are linked to (So, Kida needs to defeat Greed), and then be empowered by Royal Authority. At which point, all seven can come together, channeling their power into a powerful mage, like Merlin or Yen Sid, and then they can break the seven seals.
Royal Authority is, at its most basic level, the ability to give permission for Kingdom Hearts to be opened. Royal Authority, when hosted in a ruler, grants them the right to give a Princess of Light their 'blessing' for Kingdom Hearts to be opened. If a single ruler does not think it should be opened, and therefor refuses to grant that blessing to a Princess of Light, then simply put, there is no way of getting around it. That ruler must be convinced otherwise, or they must be defeated, and their Royal Authority claimed by another who is willing to grant the blessing.
Something to keep in mind is that, Royal Authority isn't really meant to be a major plot point until KH2. As of right now, Young Xehanort is just spreading evil, being a bad guy, trying to spread darkness and all that. He isn't really at the point where he has that 'big plan'. That's on Old Xehanort, who will make his first appearance come the Organization storyline.
So it's not really meant to be central to the plot right now. There will be moments where something happens with it, but it's much, much too soon to be worrying about who has Royal Authority. So if Maleficent is trying to find it in Tarzan's world, and Kerchak has it, then it will most likely leave the world entirely come the end of KH1. It may stick around for a while in Tarzan, but...
If you think of Kingdom Hearts like a semi-sentient will of the universe, then it would not want one of the Royal Authorities to remain in a place that not only have agents of darkness already come looking for it, but have already killed its host once. That means they know it's there, and Tarzan, and everything he loves, would become a target.
The original idea was that every wielder of Royal Authority would have a direct relation to a Princess of Heart, or at least, for example, as direct as Mulan and the Emperor are. The only exceptions would be whatever is going on with Uther, and then Mickey... for literally no reason other than it just wouldn't make any sense if Mickey Frickin' Mouse didn't have Royal Authority as King.
However there are explanations for both of those cases. With Mickey's explanation being, Royal Authority would remain hosted inside a King of great power, with a heart of pure light, like Mickey, who already does so much to keep the worlds safe from darkness. So despite him not having any direct relation to a Princess of Heart, he has been, effectively, PERMANENTLY entrusted with Royal Authority.
Probably because there needs to be one instance of someone wielding Royal Authority, who doesn't have personal ties to the Princess of Light they bestow their blessing on. As a father is more likely to say yes to a daughter, for example. Mickey must make the decision of granting his Royal Authority to a Princess of Heart, completely without bias.