This guy spent years into finding a solution, almost lost all he had and improved lives of many (both from sanitary and economics points of view). And he didn't this because he wanted to create the next unicorn. He deserves all our esteem and he certainly has mine.
I wouldn't expect this man to know about these cups or women in rural India to have convenient access to not only the cups but also to plastic bags, clean water, and soap. For those who do, however, my solution is lasting, secretive, and feasible.
http://divacup.com/how-it-works/care-and-cleaning/
"Remember to empty and wash your DivaCup at least twice a day, a minimum of every 12 hours.
If you are unable to wash The DivaCup after removal (for instance when using a public restroom), wash your hands thoroughly before entering the stall, empty the contents in the toilet and simply use a dry or damp tissue to clean the cup. At the next convenient time, clean as per the above instructions."
As far as how it would work in rural India, dunno, as long as you have regular access to soap and portable water.
Any product that's low on water use is going to be highly preferable for these women.
You and me. I did know a few people who told me they can smell menstruating women... I simply didn't ask how that's possible.