-- "Sway" is indeed a top 15 song choice, you're dead right. hell, it's probably top ten for me.
-- I don't like Goats Head as much as you do, but I agree with many of your points; it's an awesome record, and moments like the chorus of "Silver Train" and the verses of "100 Years Ago" are among the best in their discography. The vibe's great; I just wish there were a few more solid classics. As you said, "Hand of Fate" would be FANTASTIC in context.
-- "Tumbling Dice" is by far my favorite song of theirs, but "Gimme Shelter" is probably inarguably their peak. the rest of your top five is great too, although I'd replace "Wild Horses" with "Let It Loose" and "100 Years Ago" with "Sympathy for the Devil".
-- agreed on the three classics on IOR&R
-- you like the 90s albums a good bit more than I do -- they have their moments for sure, but they're way too damn long!
-- Exile is my favorite record ever, so I'm a bit sad that isn't your top pick, but Sticky Fingers is still probably in my top ten, and my second-favorite of theirs, so I'm not too upset.
-- I've always found Emotional Rescue underrated. It's utterly ridiculous, but also weirdly listenable and incredibly fun.
-- on the other hand, I've always found Aftermath OVERrated; beyond "Under My Thumb" and "Paint It Black," I find very little worth returning to very often, especially in comparison to Flowers or Between the Buttons.