Hey there!
I too am in love with the 1 & 9/16th nut width. I have come across a lot of gibson's with this nut width in my hunt, but I will start off by saying you have almost 0% chance of finding a modern Gibson or Epiphone with this nut width. To my knowledge there are only 2 modern gibson's with this nut width, being the SG Naked Model, and the Angus Young signature, both are incredibly hard to find (the angus young's more common but quite expensive).
As for vintage guitars (that are affordable):
There's some variation between an ultra small neck (both narrow nut and narrow profile) and a chunky baseball bat (narrow nut + big C neck).
If you like them fat, the 60's Epiphone Olympic's are your best bet and most affordable option. I have had 2-3, make sure it's the one with the batwing headstock and wilshire style body, some of the others can have wider nut widths etc. Another somewhat affordable option would be the late 60's SG Melody makers, they're a bit pricier than the olympics but not by much. I have one of these as well and its a super comfortable neck, a bit slimmer depth at the nut for comfortable chords, but gets quite chunky by the 12th fret.
If you're looking for a narrow nut and slim neck, I had a 1969 ES330 that had probably the most comfortable neck ever. Very un-intrusive, just lets you breeze across the neck and super smooth feel. That one will be a bit pricey though, and a more affordable option would be a 70's Gibson ES320. These are a bit of an oddball and not many people know of them, they are the brightest and twangiest gibson you will ever play even being a nearly complete hollowbody. I ended up selling mine because the neck profile (while having the 1&9/16th nut) was too much of a slim profile for my taste, almost like an ibanez wizard with a bit of a flat spot in the centre on the back of the neck.
Hope all this info helps! Trust me, I am in the same boat as you constantly looking for the right profiles, I'm a heavy thumb-wrapper so I need the narrow nut!
