As a martial arts instructor, you're definitely in the arena where I never miss.
The successful pickups I've seen work one of two ways. Either the guy is really good at martial arts and automatically attracts the admiration of the men and the attraction of the women, or they work game right before and/or right after class. In our classes, there are pretty regular times that I lot of the students will go grab a bite after class, which may be a good time to get her out of the MA class and out of the element of any of the high level martial artists, in other words levelling your playing field.
I've seen a lot of the talented MA'ers crash and burn cause they were so busy amoging that they turned the girls off, but in my experience most of the talented fighters/artists don't need to try to show you how good they are, something that usually attracts women. In fact, when I first started learning Game, I realized it was mainly about making the me off the mat be the same as the guy that's on the mat.