Couple of comments...
Rhythm man is right, you should have a slight back bow, which means the neck should bow slightly away from the strings in the middle of the fretboard. I think around .010"-.015" is the usual recommendation, I can look it up if you need the exact specs. To check it, capo the 1st fret and push the top or bottom string at the last one, you should be able to slip a business card or credit card under the 8th fret, that's enough back bow. A perfectly straight neck will usually tend to buzz at really low action.
Johnny Winter plays a lot of slide so he probably sets his action a bit on the high side like I have to. Otherwise the slide bar bangs on the frets and makes a lot of unwanted noise. I keep my action set so it's 1/8" or just a tiny bit more at the octave. That's about the same as Clapton and Jeff Beck setups, which I found in a good article in Guitar Player magazine a few years ago. Someone else liked it better t5han I did so I don't have it any more, but I remember the settings, checked mine and it was already almost exactly the same as theirs. Johnny probably has his set about the same since he also plays a lot of slide, which requires higher action.
He is also dead on about the truss rod, NEVER more than 1/4 turn and let it settle in at least overnight, I too prefer a couple of days. It may also help to give it a drop of oil (ONE drop) and let it soak in overnight before adjusting. I try to give mine a drop of oil about once a year so they don't rust. Regular light oil like 3 in 1 or gun oil will do fine.
Also you might check with a couple of guitar stores, I had the exact same problem with a Les Paul copy years ago and found out a wide travel bridge is made for the Gibson tune-o-matic setups used on your guitar. It gives the saddles more adjustment room for situations just as this. You can also remove the individual saddle and reverse it so the flat is facing the bridge pickup, sometimes that gives you the extra adjustment travel you need. I did one just a few days ago on a guitar someone brought me to fix.
Nut slots should be cut right at the factory on a new guitar, to check it by fretting at the 3rd fret and measure with a feeler gauge. In general you want .005"-.008", higher and it will tend to pull the strings sharp when fretting open chords, lower will tend to produce buzz.
FRETS is my favorite guitar maintenance site, excellent info, their page on nut height is
Here
I wish they would change the link color on here, the grey they use doesn't show up well...Anyway FRETS has a lot more info on just about anything you want to do to your guitar, usually with excellent pictures. It's always my first stop for good info.
Always use new strings when setting action and intonation, dead strings will seriously affect intonation.