If you have a JS neck it should not be too hard to get the measurements.
Radius 7.25"
Nutwidth 1 5/8"
You already know. Then get one of these:

Measure thickness at 1st fret and 12th fret. The difference between the two
is called taper usually 0.65-0.70"
Then take some soldering iron and put it around the back of the neck at the 1st
fret, from upper fretboard edge to lower fretboard edge. Then trace it on a
piece of paper, my guess would be a C-shape.
Good luck,