Your message may have the key. You quote "which has very strictly reduced my consumption of oils and fried foods. " It seems that you say you've had oils? And fried foods until recently May. Anything fried is dead food and to fry usually means oils of some sort. Unless you've always had olive oil then you can safely assume that you've gotten additional cholesterol from the oils you've used. Additionally as some else has said the body manufacturers cholesterol from its diet.
But last but not least not all Gallstones are cholesterol based, a very high percentage like around 90% are but not all, you may fit into the other category.
Dead foods means dead enzymes and building blocks of life, all of these would normally help your metabolism and your body function better. That's another reason processed foods are so bad, basically all the good stuff has been killed or deactivated.
Anyway try the flush you got nothing to lose other than some stones.