The nut is absolutely fine - my strings run closer to the fingerboard than that at the first fret and I have no issues.
First of all, realise that buzz heard acoustically is completely irrelevant - unless notes are actively choking out, the only thing that matters is whether you can hear it plugged in. This isn't a Martin D28, it's a Jackson for chrissakes, one designed for weeedly sqweedly metal. :lol:
Get the strings to pitch and get the neck straight. You don't mention how you are sighting down the neck but you should be looking from the headstock end towards the bridge. The other way round tricks the eye and makes it think it sees curvature where there is not (this is to do with how your eye focusses and processes information apparently!) and the carved top nature of the SLS exacerbates that.
Once you have the neck straight, give it a play. it's important to reset all of this to zero because (particularly if you are not confident about what to do) starting from a fresh baseline lets you see and therefore learn what the process is. It's how I started out with all my setups.
If it is buzzing, find out where it is buzzing - it's quite easy to get confused and think it's coming from a different part of the neck! When setting up I run through chromatic scales - finger 1-2-3-4 patterns from the thickest to thinnest strings starting at the first fret, then fifth, then ninth...you get the idea. This a)sounds every fret cleanly, so you can spot if there are any flat spots on your frets and b)is great practice for alternate picking. Unlikely unless the guitar is from the 90's or you've been playing lots of Korn with massive strings and no talent.
This isn't reading terribly well. I'll maybe write this up for the site next time I set up a neckthru guitar.
So, we have a straight neck, in-tune guitar strings at pitch, and we've figured out where the fret buzz is.
If the buzz is at the first few frets then the neck, as you already pointed out, has too much backbow, or truss rod tension. Loosening the truss rod and allowing the strings to bow the neck to a degree should help. But go canny, you really do NOT need a lot of relief, because the miracle of TOM and Floyd Roses is that they are height adjustable. Give the neck the tiniest bit of relief (we're really not talking much here) and raise the bridge very slightly. Tune it all back up to pitch, do your ascending chromatic exercises and see how things feel. If it feels particularly high around frets 4-9 you've overdone it on the relief - if it feels high around the last few frets you've overdone it on the bridge raising.
Make sure you pay attention to high the strings are off the fingerboard on the treble and bass sides - remember the bridge is adjustable on each side!
The fact that you have a set neck or whatever it is and not a bolt-on reduces the amount of options but makes setting up easier - normally I'd consider shimming a neck but you need not worry about that!
Hope that was of help and not a case of tl;dr!