Hasn't this already been invented? With the problem being that most westerners don't like the solution because it looks unfamiliar:
* You install a squat toilet
* It's cleaned by flooding the entire
toilet area with water, which once
turned off all washes down into the
toilet
* No toilet paper, you clean yourself
with water
The biggest problem is not even that it looks unfamiliar, but that the majority of “westerners” have insufficient ankle flexibility to squat, due to a lifetime of sitting in chairs and no experience squatting.
You might be able to build a squat toilet where the feet rested on a ramp (i.e. raised at the heel side), though I suspect most Americans would still refuse to use it.
You don't need a ramp to squat on tiptoe. I squat with my feet flat on the ground, but I have been told that doing that is hard for most (US) people. Still, Americans do squat. They just don't do it with flat feet.
That comes pretty fast with time. I was surprised I could crouch like a baby, after 3 monthes, something I couldn't do anymore for decades. I believe your back will thank you too.