I had to modify my Warwick "Just-a-Nut" to get it lower, but I did so without touching the string slots. I simply sanded the flat underside of the top section, and also reduced the height of the location pins. Probably took 0.5mm off of the bottom of the main block and from each pin, which was enough to get it to where I wanted it:
View attachment 7475570
I think the Sadowsky nut is a slightly different design in that there is a single locating tongue/groove through the middle, but the principle should be the same. I would definitely advise against messing with the slots and their relative positions/depths unless you have to. YMMV