There's nothing I like more than someone who USES their mind--and you fit the bill! It's great that you are questioning, thinking, innovating, and generally pushing the envelope here. The world needs more people like you.
I will mention a couple of things that came up as I read your impressively thorough reply.
1) Don't forget, the stones have been analyzed by many people's labs, and the results have come back as mostly cholesterol (>90%). Olive oil contains negligible amounts of cholesterol, according to Agnes.
2) Granted it's possible that the digestive juices vary from person to person and from day to day, so ever so possibly this could explain why people sometimes do not get any stones on a flush. But isn't it interesting that people usually report getting empty flushes after many flushes. I know occasionally a first time flusher gets nothing, but it seems that many who have done lots of flushes report this happening later.
3) While it's very true that you can never know if someone is posting a lie, if the preponderance of posts from apparently many folks al show the same or similar results, one may be tempted to place some faith in their thoughts. I know, if everyone was jumping off a bridge would you? I know, it could be an elaborate hoax (I'm NOT being sarcastic here--seriously!). So I think you have good reason to doubt all that you read and every reason to continue to think and innovate for yourself.
I think your idea of creating a dye-based test is absolutely smashing, if you can pull it off. Then, as you say, everyone can try it for him/herself and know the truth.