Track and replace a t-shirt design on a moving, distorted garment
Nuke's Smart Vector toolset is built for this exact problem. I see you tagged After Effects, but you did not specify that After Effects is needed. I've done this a few times before and Mocha is your best bet for AE, but as you already know it has it's limitations. Nuke can actually track the creases and folds (though of course it isn't perfect). The biggest factor I've seen in my tests is shot duration - the longer the shot the more the vectors get all messed up. That said it can sometimes do magical things! I believe you can rent Nuke for a decent price if you just need to do one shot.

Here's a tutorial showing how to replace part of a shirt. It is a bit older, but because it addresses exactly what you are trying to do I thought I'd link it: 
                
            

If you absolutely need to use AE I would combine a mocha track with a puppet warp which is hand-animated. Using Mocha you can stabilize the footage, overlay your logo and keyframe the puppet warp, and the re-track it back into the original footage.