I was thinking that the G measurements might be better due to scale length. The measurements are not vastly different.
Looks like the string action (set at the bridge) is a little high on the bass side, and about right on the treble side. It also has a bit more relief than Gibson recommends.
I don't think you need to worry about the nut until you get the buzz out with the capo on. Normally it should come when the relief and string height are properly adjusted.
Before adjusting the nut check these potential sources of rattle:
Nuts around the tuning pegs are not screwed down tightly. Fix: tighten down the nuts.
On the bass strings, the bronze wire wrapped around the steel core has a break in it somewhere. Fix: Change the strings.
These may seem unlikely but they have both happened to me.
If you still hear rattle tighten down everything else to make sure it's not a sympathetic vibration.
I also wondered if you can identify where the buzz is coming from on the fretboard. Normal string buzz results from the vibrating string making contact with the fret(s).
You've tested for a popped up fret. You've leveled... That makes me wonder the strings may be too close to the fretboard up near where the neck joins the body? The truss rod will bow the neck, but not evenly. It bows less where it bolts on...and even out a ways.
If that's where it is buzzing on yours you might try the taper trick in this video:
People generally do this to get a faster action. I generally do this at the 12th fret. He does it at the 9th as well.
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