My other goal is try not to make a fool of myself at the range with my first muzzle loader...
You will be fine.
OK FIRST, the key to a proper paper cartridge in you Artillery/Sergeant's Carbine, is the
Former, combined with the type of paper that you use.
Here is a chart showing how to make live musket rounds.
Here is how to make blanks and not use ties nor glue. Pay no attention to the dimensions as they are for Civil War blanks. The process though is the same.
Making Blank Paper Cartridges
So you want to start with a 5/8" dowel about 6" long. Now some folks like newsprint, and some like "book paper", and some like heavy linen bond...,
I like to use "book paper" for live musket ball, and newsprint for birdshot. I go to the library or the supermarket/Dollar store and find a hardback book on sale for around one dollar, and use the pages to make cartridges.
So first take the bare former and see if it will fit inside your barrel at the muzzle. You need to only insert about an inch of the former into the muzzle. It probably won't fit or is very snug. So you know if you wrapped paper around it to form a tube, that tube would not fit. So you sand down the dowel until it fits without any pressure to force it into the muzzle.
Next...,
You take a piece of whatever paper you're trying, and cut it to the proper shape. Then roll it around the dowel. You have to adjust the dimensions of the cut paper to give you two layers (two revolutions of the paper going around the dowel) at the bottom end of the cartridge. THEN you take the paper still wrapped around the Former, and insert the paper wrapped former into the barrel of your musket at the muzzle just as you did with the bare former. It probably won't fit. So more sanding until the dowel with the paper wrapped around it will fit into the muzzle . It should fit without having to force it.
Now you have a Former that is fitted to use that type of paper to make a cartridge tube for your musket.
Next...,
You close off the bottom end of the tube, and put a musket ball in, with the sprue facing the open end of the cartridge. Does it fit? Do you need to push it down the tube, while it flexes the paper outwards? Does it "just fit", or does it drop in easily and sort of have space around it?
You want the paper tube on the inside to just hold the ball, not needing pressure to put the ball into the cartridge (that means it will be too big for the bore) or too small that there is visible space left around the ball (that will reduce the accuracy).
Next...,
Once the ball is correct, you recheck the fit in the bore using a cartridge tube with a ball within it. It should fit just as before.
IF it doesn't fit, if it's too tight, you either a) try thinner paper, or b) try a smaller ball.
IF the next size down on ball (I have a custom .590 mold) is too loose, you sand down the Former until the cartridge hold the ball without any gaps between the walls of the tube and the ball. This will likely give you a cartridge that is too small for the bore when checking the ball/cartridge fit at the muzzle, SO... you try a larger piece of paper and three layers at the bottom end, OR you try thicker paper.
Eventually you will find the right dimensions for your paper with your ball and the right thickness of paper when wrapped to give you a good fit to your bore.
LD