The best way I have found to do final barrel fitting by hand is with a scraper, such as this one:
https://www.muzzleloaderbuilderssupply.com/mbs3cart/agora.cgi?cart_id=9801410.12690&p_id=25585&xm=on
They are available in various widths, the wider ones are best for the bottom of the channel and I use 1/4" for the sides.
I start by using gouges to rough out the channel, then inletting chisels with inletting black once I can start to get the barrel into the channel. Near the end of the job, the scraper makes for a nice way to remove trace amounts of wood and blend without leaving behind chisel marks or over cutting. The diagonal flats and the bottom of the channel don't have to be perfect and there is some forgiveness if you remove a little too much wood here and there as long as you don't go so deep as to interfere with the ramrod hole and where your lugs or staples will be. But, you want the sides to be so snug that it looks like the wood grew around the barrel. The breech also has to be perfect for durability and accuracy.
For chisels, you can spend a fortune on them, but I started with a basic Flexsteel kit from Woodcraft that was affordable and had most of what I needed. Like anything else, you get what you pay for so invest in good quality tools whenever you can.
Here's a tip for inletting black. I found the commercially available inletting black to be too messy to be practical for the barrel. Instead, use a hurricane lamp available at most hardware and department stores. Turn the wick up so that the flame is large and smoky, and pass the barrel through the tip of the flame a few times. You get a nice thin coating of soot that doesn't make near as much mess and is a lot easier to reapply and clean up.
Some might growl at this, but don't be afraid to use glass/epoxy bedding, especially for your first build. It will take care of many mistakes and imperfections and will help with accuracy. However, if you decide to do bedding, try not to have that in mind as you work. You can find yourself getting lazy and counting too much on the bedding.
Good luck, I think every builder should have the experience of inletting a barrel by hand, at least once. If nothing else you will gain tremendous admiration and respect for the original masters.
