I haven't read the whole thread, but I think the Stones found their own voice from Beggars Banquet through Exile. Those four albums there are incredible. After that, Some Girls was great as well, and maybe Tattoo You. The others before, in between and after had their moments but not all.
One thing I have to admit though, is that the Stones' Their Satanic Majesties Request is so bad, it's good. I mean that in a most complimentary way. A very bad attempt at making their own Pepper's, it falls woefully short, but as much as they dismiss it, I have ...