I think you are on the right track, and not to speak for David but here is my advice:
Play the proper not values to the beat. If you use a metronome, which you should to get the proper timing, you can play the riff slowly and focus on using your picking hand to quiet the tones that are not meant to be played.
This was the issue I find most people have when learning this riff. The speed and the cleanliness. I seem to use my thumb and my palm, i think to keep only the right notes ringing out.
Also, I think when Slash plays this, he has his tone knob turn almost all the way down. It helps to make everything crisp.
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