OK, for comparison:
A Heavy Blaster Pistol specialist does not learn trick shots like "Three-Hit-Ricochet" or "Silent Shot". A specialist in Vibroblade does not learn a "Dragon Whips Tail" special attack that lets them attack three opponents without penalty.
The specializations allow you to get better at something that the base skill for half the character points. So, you sink points into the specialization for heavy blaster pistol. You're then better with heavy blaster pistols than regular blasters or blaster rifles. The specialization (which limits you) is made up for by being better with a sub-category of weapon. It doesn't give you extra tricks, one-shot kills or special defences. So I use that as a comparison for what is allowable under a specialization.
So, I will not allow someone to spend half the character points to improve a particular form of brawling, and become way more deadly with that dub-class than someone who specialized in heavy blaster pistol. So, on it's face, the special moves of martial arts are a non-starter in the rules as written. Special martial arts rules are also not part of the core rules - they were printed in specialized supplements.
So, on it's face, special moves are a non starter.
However, I like the flavour. Teras Kasi, Echani and Hapan martial arts are part of the extended universe for Star Wars. Martial Artists exist. But it is way to overpowered to make them part of what amounts to a weapon specialization. So, I tried to find a way to incorporate special moves into the game that did not break the point of specialization. I allow you to take the special moves as an advanced skill.
Both Ben and Corey have mentioned you guys take martial arts, and you have both compared the strikes and moves you learn to the game rules. I think that's not an appropriate comparison. Think of the martial arts you learn at your weekly class as the baseline martial arts skill. But true practitioners can perform heroic feats like the Kung Fu warriors of legend (like Crouching Tiger, Hidden Dragon). THAT is the point of the Martial Arts (A) skill. So, a Teras Kasi master can increase their attributes, become deadlier, quicker and tougher than is normal for a human. A master of Hapan martial arts can strike out with a single kick and hit three opponents faster than the eye can see (in a single segment of combat time, as opposed to three separate actions). A master of Echani martial arts can leap and spin through opponents faster than the eye can follow. These are heroic feats, and I envision them being beyond those who merely practice martial arts. A master of the Martial arts you are developing, Ben, can kill someone with a single strike (if they strike from surprise) regardless of armour or protection. You have specials that make you quicker, harder to see, and deadlier than someone with a standard "once a week for an hour" martial arts class. Special moves are a mark of devotion to the study of that particular art.
And you can pick up moves from more than one art, if you find a teacher and learn moves from that style. Want to walk up walls? Balance on a tiny tree limb? Fly through the air? You can build a martial art around those moves, and perform these heroic feats.
Also note that when you do standard martial arts fighting (no special moves), you combine the martial arts specialization with your martial arts (A) dice, meaning your advanced study makes you more effective with even the basics than a novice. The Martial Arts (A) moves only use your Martial Arts (A) dice, but your damage and standard attacks / defence are rolled normally.
I definitely see a place for martial arts moves in the game, but not as a specialized form of brawling. To get the advanced martial arts moves, you need to devote time to studying it, as an advanced skill. I haven't heard anything so far that makes me thing otherwise. And I'm not going to give a brawling specialization more advantages than someone who specializes in heavy blaster pistol.
So, the options are special moves becoming available as an offshoot of a dedicated study of advanced martial arts, or they are removed from the game entirely. I'm certainly not about to work out a bunch of trick shots someone with Heavy Blaster Pistol specialization can do.
Now, having said all that, I can possibly see a case to remove the Offensive / Defensive split. And the Silent Kill DC you and I discussed over e-mail may have been a little high, comparatively. But I think the overall premise is sound, and I haven't heard anything so far that convinces me otherwise.
My ruling stands. I'm still open to continuing discussions about this topic, provided you have something to contribute or a new perspective to the discussion that hasn't been covered already.
If you guys seriously see no value to this, then we'll yank the special moves entirely.