At this point, it seems late already especially if that rotting part is not healing properly. But if you want to experiment further, after all what have you got to lose, try and graft it. If your temps are still warm, it may still work. But typically it is better to do the graft when overall temps are warmer and with a healthy scion. So maybe you need to put it on a heating pad. If it grows, well and good, if it still fails..at least you tried.
Then get an ordinary moon cactus locally, observe the growth of that plant and learn from it further.
