Hello again!
I doubt the Riff Raff would be too bright for you unless your guitar is pretty thin or doesn't have much natural low end. It's bright but not piercing or thin by itself. That said, the Mule bridge is more balanced overall, so will feel slightly fuller. The real difference is how they feel - the Riff Raff is crisp and bitey, whereas the Mule is "crunchier", if that makes sense? A softer attack, but in a very nice way.
Alternative thought - get the best of both, plus a bit more, particularly as it's something you'll be using for high gain: consider the Black Dog. It's fuller than the Riff Raff, with thicker mids and more low-end body, has the high-end smoothness of the Mule, so won't be too bright, but is still PAF-level output so it's not too hot at all. Yes it's a higher DC, but it's also thinner wire; it really isn't that different to the 61s in terms of output. It is slightly more modern feeling in the mids, which means it takes to gain *really* well, but also retains a lot of PAF character on lower gain - it's a real best of both worlds.
As for the neck, the Stormy will do what you want, for sure, but I think the Mule will do it better, especially if you do look into the Black Dog. The Mule neck isn't dark or bassy at all - it's full, creamy, but has more controlled bass than the Stormy neck, and fuller mids. They're both warm, but the Stormy neck is slightly scooped and has a sweeter high end; the Mule is more open while also being fuller. The Mule and Black Dog have very similar top end smoothness, so they'd pair well.
So I think you'd absolutely be happy with a SM/Mule combo, compared to the 61s, no doubt about it. But from what you're describing, I'd bet that the Mule/Black Dog would make you even happier. The only thing that might caution me on that is if your SG is very middy naturally, in which case I'd be tempted to go full Mule set. My SG is certainly nothing but mid-range! But if it's brighter rather than middy or bassy, then carry on as above.
