Don, you are right about alloy. You want to use alloy 25/1 or softer. I prefer 30/1. The first time I tried to muzzle load it was with some Bullets made up with linotype and pure lead, I have no idea how hard. But the first time I tried to drive a bullet thru the false muzzle I went into shock. Hurts when you give a bullet starter a whack and the bullet just barely goes into the false muzzle. I cast some 30/1 alloy bullets and all went well. Now as to size, my Pope slugs at .380 to .381 depending on where you are in the barrel. The original mold that came with the outfit casts .382 so it is groove diameter or a little bigger at the base, I have 32-40 pope molds that cast .326 to .327 at the very rear band. They shoot super breach seated with smokeless, have not tried them muzzle loaded. The scrapes the barrel clean theory is real and it does work. I have shot my 38-55 many times with black both straight and duplex loaded and after you have pushed a bullet all the way down to the chamber if you give it a little snap at the end it will fall out thru the throat and the bore will be claen and bright and shiny. This also by the way leaves a little film of clean bullet lube in the barrel in the process. 
Now as to the process. I have done this quite a bit.  I have shot a couple of 100 and 50 shot matches and doubt I will ever do it again. maybe a ten shot match where straight black is the rule. I found that my rifle shot super muzzle loaded. BUT! it is a lot of work. let me describe the routine.
First you have to shoot a fouler just to limber up the barrel and the lube in the barrel.
then you stand the rifle up, wipe the muzzle clean, mount the false muzzle. start a bullet into the bullet starter, mount the bullet starter carefully onto the false muzzle and drive the bullet into the barrel. It goes down about 3 inches. then you remove the bullet starter, and then using the seating rod thru the false muzzle seat the bullet carefully down to the chamber/throat. now remove the seating rod and false muzzle and park them securely. now you can bring the rifle up to the horizontal and look into the chamber to see the base of the bullet. Some people have experienced the seating rod "sucking" the bullet back up the bore although I have never experienced this. A shot fired with the bullet some where in the barrel other than at the breech is asking for a "Ring or Donut" in your barrel. You are now ready to load in the case with the powder charge, I use a cork wad in the mouth to keep the powder contained. You may now bring the rifle to battery and aim and fire. Now the whole process starts all over again. By the end of the day you have hoisted this 14 or 15 lb rifle up and down and done all kinds of inbetween work and you are exhausted. NOT FUN!
I shoot now with the same bullet breech seated, mostly with smokeless,
sometimes with black duplex loaded when allowed. and I do much better. That is to mean I do much better. I will say that when I muzzle loaded using either straight black or duplex the rifle shot superbly. All the Pope molds I have had the opportunity to examine and or cast from are tapered, usually from bore size or even slightly smaller at the front to over groove size or even bigger at the base band. With good lube they shoot well in good rifles. I own a couple of original Winchester 85 s in 32-40 and that big base band Pope bullet seats easily in both of them and they do not appear to have ever been rethroated since leaving the factory. Well enough for now. HTH, Regards, FITZ

Boats, Pope made the seating rod the correct length for the bullet he supplied with the outfit. It seated the bullet correctly when bottomed on the False Muzzle. On pope Muzzle loading outfits if you look closely at the barrel down near the chamber you will find a very fine scribed line. All I have seen are on the right hand side of the barrel. This line indicates the length of the loading rod to seat the Bullet correctly. Pope cut it pretty close. In the Muzzle loading outfits I have experienced the bullet is on the verge of falling out of the throat.If you seat it too briskly with the rod it will fall out. This now requires the shooting of another fouler as Muzzle loading two bullets will change the conditions and the Rifle will not throw the shot to the same zero. I have experienced this and know it to be true. Also when starting the bullet thru the False Muzzle, the action should be clean and done in one stroke. Every time you hit the bullet it upsets some more and again will not shoot to zero. I feel that all of these issues are the reason the shooting fraternity back then embraced the smokeless powder. It shot clean and did not require all of this exhausting work. Another issue overlooked is the fact that many of the great Targets shot back then were all day affairs. Shooter's did not take to the line and shoot a full record target in 30 or 45 minutes as we do now. The famous target shot by Rowland took two day's by his account and has been said by some to have taken three day's. If you want to see how the shooting was done back then you need to read "How I Became a Crack Shot" by Milton Farrow and read his description of the shooting routine at the Creedmore matches. Well, enough for now. Regards, FITZ.

I once ended up in Alexandria VA, with a few hours to kill.  I wandered into the US Patent office and flipped through old firearms patents from the early 1800's.   There was a patent drawing for a false muzzle.  As I recall, it was from 1811.      Since I was only looking in the drawer from 1800 to 1825, it was definitely from that time period.

Fitz,
Thanks for the description.
I have a couple of questions if you don't mind.

1. When shooting the muzzle loaded bullet with black powder in the 38-55 cartridge where you using regular brass or were you using "everlasting" thick walled cases?

2. If you were using normal "thin" walled cases did you experince any case stretching or seperations?
I understand in the 32-40 with breech seated bullets and straight black powder some folks have had cases stretch and or seperate.

3. With black powder did you use the same case for each shot or did you have your 100 cases already charged?

Thanks Matt