I'm glad you like the 47th site...I used to be in charge of that in college and created much of what you still see there today. As far as that article went, I merely copied it out of an old issue of Camp Chase Gazette (with the author's permission of course).
Most of what you have asked has been debated (sometimes hotly for years). Let's start with the easiest part first. With regards to the lettering of companies based on the seniority of captains. I have looked for this for years, and have never found any proof that the senior captain got Co. A., 2nd got Co. B. etc... I imaging this might have happened (how much I can't say) when a regiment was first being formed and it's officers being commissioned, but after the first deaths/discharges/promotions this would pretty much go right out the window as far as order goes.
Now for the more complicated subject. Coming onto line. My experience is based mostly on Gilham's Manual, and many manuals that came before it. Hardee's and Casey's are very similar in just about all practical respects when it comes to this matter. From the description that you have given, the only situation that I can think of that actually fits that description is when a regiment is forming line for morning/evening dress parade, and the companies come on line in a set order as they are being posted by the adjutant of the regiment (in this case you are going by the seniority of officers, so color/5th company is always referred to as color company, even when not in the line, until a major "reorganization" for lack of a better term of that regiment which might not happen until after a major battle if at all). That is all well and good for more formal occasions (when no one is shooting at you), but this is not how companies would take their place in line when actually forming under fire. Now it gets very complicated because there many different ways a regiment could be forced to form depending on how they had been maneuvered onto the field (i.e. from column of 4's, from closed column or companies,with the battalion's left companies in the lead, or right companies in the lead etc...), and depending on they need to form by different commands (i.e. on the right/left by file into line, forward into line, left into line wheel, on the right into line, etc...). Without making it too complicated, assuming that all companies are present, on the march (in one formation or another) they would be in order (1,2,3,etc...), or if marched by the opposite flank (10,9,8,etc...).
Let's see if I can manage a simple diagram here...I will do this based on a 5 company battalion to save time...the principles are the same, though in this case the 3rd company will actually be the color company. (Note I am only using -C- for the color company itself, not the exact placement of the colors themselves within the line).
Battalion Line
-5--4--C--2--1-
----------------
Column of Companies (Right Flank Leading)
-1-
---
-2-
---
-C-
---
-4-
---
-5-
---
Column of Companies (Left Flank Leading)
-5-
---
-4-
---
-C-
---
-2-
---
-1-
---
Column of 4's Marching by the right flank
---------------------------------------------
------5----------------C----------------1---- -->(Direction of March)
--------------4-----------------2------------ -->(Designations Staggered to simulate doubling of files)
---------------------------------------------
There are many more situations that can be done, but here are a basic few. I think you can see that breaking these formations to try to post in line of battle as mentioned for parade just does not work easily in the heat of battle. The different ways to form into line are designed with the ease of reforming quickly and in the proper alignment of companies while being done in a timely manner since you are most likely under fire. Basically, when the lead starts to fly, formations are about function, not about the honor or which company posts at what time.
Again, there is a lot more to this subject, and has been, and will be debated for years, but hopefully this is easy enough to understand. I hope it helps a bit.
Josh Bucchioni