Couple of things--
On lever travel and sight picture...
The aperture sight (in this application) is there to 'stop down' the exposure of light to the pupil, thereby deepening the field of view over the rear sight, the front sight, and the target.
Slight rotation over the pivot pin's screw thread should not affect the point of impact, and properly made it shouldn't significantly effect the amount of aperture.
On price to build one of these...
Take the image shown above to your local machine shop (the successful one) along with your double rifle and have them quote you on the work. You might be surprised at the price (might be less than you think)
Again, note that from maker to maker, era to era, rifle to rifle, the diameter/depth/shape of the screw head, length/diameter/pitch of the screw shank, and height above the base of the screw head to the aperture will need to be custom for each rifle. Ideal aperture size will vary from shooter to shooter depending on numerous factors, including distance of shooter's eye to the pivot pin axis and distances between front/rear sights and those to the aperture.
Much of that can be measured/calculated/experimented by shooters with little to no machine shop or craft experience by taking black tape or paper and fixing it to the rifle and fiddling away with razor knives or pins or hypo needles to get the aperture size and tape or whatever to get that aperture in the right place.
From there you're close and can work it out with your metal smith. Doing this over email or the telephone might not get you effective results.
--Tinker
