Don't make them Eastern then. No one is buying it because it's an eastern style, they're buying it because of the bonuses. Call them Fighting Mastery Style A: +3 Dodge and people will still buy it. Why? Because they want to get an extra dodge factor to help them cope with the huge ass NPCs being thrown at them at times or to cope with having a lower body. What's the real name of Fighting Mastery Style A? Who really cares? I sure don't care. I care that I get a bonus to Will or dodge or attack.
In other news, so let's say I know Open Hand Karate. Sure, it doesn't say I can use a sword, but you CAN use a weapon irl with Open Hand karate. In fact, you can easily use a staff or a sword. Thus, there are bonuses used. You don't get to add the open hand karate levels you've earned to it but you do get to apply the knowledge gained to the weapon.
If martial arts is a lifestyle, you take these bonuses with you and use them elsewhere. That's the way I read it anyway.
If the style makes you more disciplined, then there's a bonus to will. :: shrugs ::
In fact, I have a whole page of stuff that proves just that stuff, with built in pre-reqs that were created by an old friend of mine — >