This is the best reading I've ever done on a forum post. OK, I have a small world.
Anyways, I think carrots are the answer. The trick is to get farm fresh carrots with the tops attached. No, it's not about the flavour, but be patient and I'll explain. The carrots are best eaten 3 to 5 hours before the time of your normal BM deposit. It takes time for this stuff to work through the system you know. Do not throw away the carrot tops, this may be needed later. Go along with your day as you normally wood. Enjoy the sunshine, talk to the neighbours, have a coffee or other favourite beverage and then when the time is right get down to business.
Now, put the carrot tops in a bag and take them with you. Close the door, read a book, facebook, or whatever it is you do while you are busy. Once done do an inspection. If all slipped away without a trace then ditch the carrot tops in the garbage and cover with TP to hide the evidence. If traces are left, unbag the tops, wet them, add a bit of soap and then, well you know... ....give the throne a clockwise swoosh. Yes, that is all it takes. All tracks will be gone.
Cheers!