Thanks to all for your thoughts on my shredded toe problem. I know it's not athletes foot - I've had that before. This is on the ball of the toe itself, not the joints. I already have tabi slippers, and I suspect it'd be difficult to find size 13 pointe shoes. I'll try some grain alcohol if I can find it here (I'm in Japan) and continue taping as necessary.
BTW, the problem isn't that the skin on the bottom of my feet is soft - on the contrary, it's callused as all get out! The problem is that the calluses are tearing in long strips, leaving bloody stripes on the tatami.