Can't believe this topic still has the runs...
I can't add to the roll direction question, but as I sat and contemplated the other day, this thread crossed my mind, and I suddenly realized I had a useful tip regarding the TP.
And someone conveniently mentioned the paper unrolling while you drive down the road. My wife, in a stroke of genius I might add, solved this problem. And here it is, so brace yourself.
When you mount the roll, over/under as you choose, squeeze the roll so that the cardboard liner becomes an oval. Henceforth, gravity will prevent uncontrolled unrolling of the paper, yet the roll is still fully functional, albeit a bit wobbly.