How does the rifle shoot with jacketed bullets?  It’s possible it may shoot cast bullets better than jacketed. 

For shooting cast bullets, first slug the throat area. Drive a lead slug about an inch or two into the bore from the breech end and measure the OD of the slug. Use a soft (lead only) cast bullet that is larger than the throat diameter so it will swage down. 

If it’s a 5 groove barrel, you have to roll the bullet between open calipers and gradually close them until they just touch the bullet.  Your best chance at decent accuracy is a cast bullet sized to the groove diameter +0.001”. 

A rough bore is probably going to cause some leading of the barrel. I would first clean the bore of all fouling before shooting cast.   Before you shoot jacketed bullets again, clean the bore well to remove all traces of lead. 

For the first tests, I wouldn’t try and drive the bullets too fast. That requires harder bullets and may lead the bore if it is rough. It will take some experimenting.  

For shooting cast bullets or trying to get some new life out of an old barrel what you want to measure is the bullet or "ball" seat. The area cut by a reamer directly in front of the chamber mouth but not before the origin of the leade in or throat, and size the bullet and select one which allows about 1.5 thousands clearance in the neck portion of the chamber so the case can release the bullet/keep pressure down but take up as much as that space as possible.

Even in a new barrel, because of the way a reamer is made, the tooling has to cut an area large enough to allow for clearance during expansion of the neck to release the bullet but then have a piloted area small enough to create a rapid taper on to the origin of the rifling to allow clearance for the bulleted case to chamber without undue friction. The bullet seat, is minimum the outside diameter of whatever cartridge may be selected chambers neck, but has to rapidly in a very short distance allow the tool to enter the bore and begin to taper the lands, which is substantially smaller than the outside OD of a brass case. The bullet seat, stabilizes the bullet and keeps it centered in a well made chamber not unlike jamming it into the lands except the outside diameter restricts gas flow past it. When the cartridge case expands during ignition, the neck opens and the bullet floats on the gas created by the powder before it even starts to move front. With a cast bullet, the plasticity of the bullet metal in a perfect scenario should be resistant to deformation and being larger in diameter, prevent gas leakage or emergent gas from escaping around the bullet which can create leading, deformation and all sorts of mayhem. Both cast and jacketed bullets behave in a similar manner except jacketed bullets have a cupro nickel, soft steel or gilding metal envelope that protects them from higher temperatures. Keep in mind, the anneal of a brass case is softer towards the bullet mouth, than the head of the case and that very smaller cone shaped transition can be seen either on a reamer, drawing or a chamber cast made with cerro-safe or by pound casting the chamber. Or, even closely studying a finish reamer itself. It's a little short transition that's coned shaped and very short.

Emergent gas always a very small bit, escapes past both lead and jacketed bullets. Its the puff of smoke that erupts from the muzzle before the bullet is even half way up the bore or gets pushed out as the bullet travels forward.

Good write up Doco.