I assume most know about the Beach Boys 1966 Masterpiece Pet Sounds. In 1996, Brian Wilson created The Pet Sounds Sessions for the 30th anniversary Collection (which I recommend for anyone who loves the original album). It also came with a 127 page booklet.

If you had your choice of a similar project for the Stones, which album would it be (other than EOMS)? Assume each take for each track is available and the sound is a 10. What release would be the most interesting to listen to?

I would probably choose TSMR.

There's an eight-disc boot of the Satanic sessions floating around on the internet. It's pretty tedious.

I'd go with Beggars' Banquet, but would include the sessions for Jumpin' Jack Flash and Child of the Moon. The last album by the original Stones and several songs changed significantly over the sessions.

Yeah, there probably aren't many extra takes/alt mixes of anything done pre-67, because those albums were done more quickly, so I'd have to go with Beggar's Banquet and especially Let It Bleed, as these were the last of the Brian sessions, so those might shed more light on whatever input Brian might have had on these--at least on the tracks where Brian's guitar wasn't turned down and eliminated from the recording mixes...