I have not used the SL2 but I have a 6D, and the AF systems seems to have some similarities, ie the peripheral AF points are line sensors, with only the centre point being cross-type (and the 6D gets an extra vertical line sensor with f/2.8 and wider aperture lenses).
If I was using my 6D, I would largely agree with what lago has said. I doubt you would have much luck with the peripheral AF points. However I would add:
make sure you pre-focus - you don't want the lens to have to change focus by much when you want to take a shot. In fact, consider taking some shots where you pre-focus on a point and wait for the action to come to that point (ie manual focus)
when you are using AF, start the AF system before you are ready to take the shot, ie give the AF system time to start tracking your subject (remembering that if you only have the centre AF point active, you will need to keep it over your subject) for a few moments before you take the shot
if you are using a lens with IS/OS, turn it off or else make sure it is active well before you are ready to the take the shot so the system has time to sort itself out (although a recent article has suggested that with Sigma's OS, you need to do that even if you have OS off)
don't rule out using your 50 f/1.8. Shooting it at f/2 will give you an extra stop over either of your Sigma lenses, and help you keep your ISO down a bit. That assumes 50mm will get you close enough for decent photos (but remember you can crop a bit later). It also assumes you won't be so close that 50mm at f/2 will give you such a shallow DOF that you don't have much chance to get action shots in focus, although even then I would try at least a few shots like that given it sounds like you will be shooting in pretty dim light and you need a fast shutter time.
I wonder whether 1/200th will be fast enough to stop the action, but I don't have experience with martial arts specifically so I'm happy to defer to lago on that.
I see other people have suggested using liveview. As I said I don't have any experience with the SL2 so I cannot comment on that. It may be it is the way to go. Otherwise, though, I'd go with the above approach.