Recreating The American Longrifle  IMO is a very good book . Not as fancy  as "The Gunsmith of Grenville County."  But  its what most all of us older smiths and builders started out with . You have to look at it as a book . The book has an order . You build in that order . If you try and take the chapters out of context of that order , then your going to get confused . Not to mention things become complicated . Once you understand the basics  and how the placement of each component  effects the placement of another , then you can start using the book as a reference 
Your transitions should start  up at the  center of the  tang screw .
 Drop and cast  is not an case of ; it is what it is .
 These are things that are specific to a given person  or a given style of shooting .
Today production manufactures  build for an average  shooter ..
 But by trying to work this out now , you are jumping ahead  and thus your  becoming confused .
 You need to start with understanding the why  of things .  
I would like to follow the lines of the LeMann but man... that butt... it has to hurt,
  That would be true if  one were to shoot that style of rifle from  high on the shoulder . But when we understand that  the rifle was designed to shoot from lower on the shoulder to top of the arm , we then see that it wont hurt . We also then  see that the very deep cresant  shapes , must be shoot from the arm , not the shoulder 
 See , once we start to understand  the shapes We can even then go to the extreme  and understand  why the evolution of some of the very deep  butt plates  on  some target rifles 
.  See by understand that many of these were meant to be shot from under the armpit . IE a laid back , backwards prone position , not off the shoulder . 
  As such this shooting style effect the drop  and the cast . Today  people are built differently then they were 150 years ago .  We are taller , heavier  and in some cases our necks and arms are longer . that’s where the drop comes in .
 Let me see if I can explain this to you . When you shoot a rifle that’s been designed to be shot off hand , for a specific person , that rifle , when  brought to the shoulder , should yield the  persons eye  to instantly be  inline with the sight . The less movement , the shooter has to do to make that alignment the better ,IE leaning forward or tilting the head to the side . Thus if one has a short neck , their drop will be less then someone with a tall neck . Same holds true for cast  in that a person with wide shoulders  often needs more cast then a person with narrow shoulders . Now add in a gun designed to be shot from the arm  and not the shoulder and  you can see that  such a gun would need even more cast so as to reduce  the shooters need to hunt for the sights .
 Next  consideration come style of shooting . Is the gun designed to be shot with a forward facing stance like  a shot gun  or a more side type of stance with the  shoulder  in the same  direction as the target . IE the gun runs more across the chest the away from it .
 Once you understand these things you then can  decide of you drop and cast .
  You also will then be able to look at a given rifle and understand  the type of person it was made for and how it was to be shot . As well as why the rifle has the lines it does 
I like the lines of the one ridjrunr posted in reply to one of my questions... but this is going to be a flint... I think...(I have only changed my mind four times to date.) 
 there is this misconception that all half stocks must be percussion guns . this isnt true .
 the Hawken Bros did not invent the half stock rifle . in fact the lines  of their guns  wasn’t even  innovative. Even if we   hold the conclusion that they  did do something special , they basically only re invented the wheel  as  the plains type rifles very much  resemble the early European  half stock sporting rifles .
 Here are some  other ½ stock rifles for you to look at . As you look at these , try and look past  the gun and look at the details of the gun . Notice the differences in the barrels 
Some are round , others swamped , others tapered . Notice the differences in the drop .  Look at the butt plate designs and see if you can understand how the rifle was ment to be shot .
I am also including a photo of a gun made by Gustuvus Erichson in Texas  in or around 1838 .
 Notice the gun is a ½ stocked flintlock . It also carries a longer swamped barrel .
 Notice the drop of the  stock . See that the butt plate isn’t  of a design that’s  shot off the shoulder ?.
 This tells me that the person it was built for  most likely  had a tall neck  and did a lot of off hand shooting .
As such , even for it length ,  for such a person , the rifle would have been quick in the draw 
Gustavus Erichson was a gun maker, gunsmith, and gun dealer in Houston from 1838 until 1872. Two of his sons, Otto and Alexander, continued the business until the 1890s.
An amazing rifle has just been discovered hidden away in the vault at the Sam Houston Memorial Museum in Huntsville, Texas. An original flintlock rifle that appears to have been stocked in Houston as early as 1840 and stamped G. ERICHSON HOUSTON. TEXAS. on the lock and the barrel. Mounted in iron with a pewter nosecap, stocked in walnut. This large rifle measures 61 inches overall and has a 43 5/8", .51 caliber, swamped barrel. The rifle is in fine shape and, at this time, is the only known Texas marked flintlock sporting rifle.