This is a special 3-48 x 1 inch screw mounting kit complete with brass ferrule and press fit nut. The escutcheon (ferrule) and nut are both press fits into a 1/4-inch mounting hole, which should only be deep enough to bring the edge of the nut or ferrule slightly below the surface of the grip. The grip needs to be thick enough to allow at least .050 inches of material for the ferrule or nut to push against. More thickness is stronger and helps prevent the material from allowing the nut or ferrule to pull through if the screw is over-tightened.
The height of the nut or ferrule is 0.115 inches, so the .248-.250 diameter hole should be around 0.120 deep in order to keep the edge of the brass just below the grip surface. This allows refinishing, polishing and sanding of the grip without contacting the nut or ferrule. Buffing and polishing the grip surface might pick up a black smear if the buffing is done across the top surface of the brass. Brass can do that!
These fittings are slightly more expensive than the No4 and No2 sizes due to the relative difficulty of getting the 3-48 fillister screws in 1 inch length, and the fact that the volume or demand for this size is low, meaning production of the fittings is done in smaller quantity than the extremely popular No2 and No4 sizes. Running a CNC machine to make 100,000 parts is a lot less per part than running 100 of them on a Swiss Screw machine or turning out 100 of them on a tool room lathe! The set-up time can be twice as long as the actual production time, for small quantities. But small quantities are what people buy in this particular part. When needed, it is really needed. Otherwise, the 4-40 would be a better option if you don't need to use this size of thread and screw.
The No5 size is about 1/10 the popularity and sales volume of the No2 and No4, and the sales volume of the No3 is about 1/10 that of the No5 -- so you can see that a fellow would be silly to try and stock as much inventory to sell in No3 size! But at least I can keep them in stock for you when you need them, without having to make one at a time!
I do have a 3/8-inch 3-48 screw length if you need a short screw, but then again, you can always cut the 1-inch down to any shorter length and grind the tip to make it look nice again.