The Jedi Iroh
So, yeah, I know there's a lot of distinction between these in the martial arts world, with more than a fair bit of disagreement on if they're real, or what they mean. However, with this being a Jedi/Force sensitive-centric organization, I think it could likely work here. Not in the same way, per se, but in their emphasis.
As the Way of the Light Hand focuses on self-mastery and combining the strengths of many forms, I'm going to try and split it up into different portions and philosophies of each style, based on what tiny fragments of info might exist on them.
First, is the distinction between hard/soft and internal/external. I think we could probably plot them on a XY axis based chart, if we wanted to visualize it.
Internal-----External: For this one, I'm thinking it would be a lot on the philosophical focus of the style that it was designed around. Mandalorian fighting style, for example, would be external, as it is a very practical style evolved specifically for fighting. The Echani Art, on the other hand, could be seen as being more internal- as its emphasis is on developing mastery over the practitioner's body. Zama-shiwo also appears to be a form of inward style. So perhaps then, internal and external styles are based on the purpose/emphasis for the style is.
Hard----Soft: This one, I'm thinking about its philosophy of movement. Whether it emphasizes direct or indirect applications of force. Shockboxing, for example, would be incredibly high on the Hard side of the spectrum. Tae-Jitsu more soft, I think. Teras Kasi probably somewhere very close to the center, based on its description and its IRL inspiration from pencak silat. Bakuuni Hand, probably also hard style, but its use of the Force enhance one's own strength would make it more Internal.
So, that's my sort of very rough sketch of how we can use these. Thoughts, critiques, suggestions?
I haven't done a ton of extra thought on it all, but it seems like there's a decent chance of it working out. The challenge of course is how only vaguely fleshed out things are for most Star Wars martial arts styles.