Warrior/Courtier/Mystic
Warrior and Mystic are not Japanese words anymore but Courtier also never was a Japanese word... So why not... I like it!
Both warrior and mystic feel like change for the sake of change. I doubt that the target audience had trouble with either samurai or bushi, and shugenja isn't really that hard of a thing to explain.
You do realize that the start of the thing was to get rid of the Monk and the Ninja keyword, because they are faction specific?
Another solution would be to have more Monks and Ninja in the setting.
Crane get the Harrier back, now with Ninja keyword. Mantis also start to train Ninjas, they have stolen half of the Scorpion clan icons anyway and for historical reasons Lion Ninja in white are a thing...
The Unicorn (they adapted the tatoo thing from the Dragon) and the Crab (Hida Nichi) start opening up Monk orders and the Asako order grows.
Either direction is a good one because having a keyword with lots of card support which only two clans have access to is not a good thing.
Or they could not water down clan specific themes and just give kickers on actions that are performed slightly better by ninjas and monks, and keep those keywords in the clans that currently have them. Anything from increased effect to reduced honor loss would work. You can have a bushi type ninja, a courtier type ninja, and a shugenja type ninja, there have been in the CCG in the past. You also have monks that fall closer in line with one of each of those three spheres. Handing out keywords like candy in places where they don't make sense or fit was one of the big frustrations people had with EE.
There could also be a very small but style defining set of actions that key off of the niche classes could work too, they'd just have to make sure not to either over or under do it.
Warrior sounds like it belongs in a western themed RPG, not L5R.