On the other hand, converting sign language to text/speech seems like it should be quite straightforward. Not knowing anything about sign language, I'm assuming signs map (more or less) one-to-one with words. The input from LEAP appears to be extremely high resolution, so if the sign gestures are properly normalized (and judging from the demo video, it looks like the LEAP SDK itself already does a good degree of input normalization), you should be able to just train your classifier (neural network, SVM, etc.) right out of the box.

Of course, things are never as easy as they look so in all likelihood there are plenty of complications I'm completely overlooking at first glance. But I agree with you 100% that it sounds totally doable.