Hi Paul- showing a .547" bore and .571" groove to groove showing .012" deep rifling, means your bore is larger than the standard .540" & it has standard depth rifling.
For us, a .540" ball would be perfect in this oversized bore as it is already .007" smaller than the bore, whereas a .535" ball would be perfect in a .540" bore measurement - for a hunting or trail walk rifle.
Your barrel, being approximately .07" larger than standard, means a larger ball than standard is required, not small as you thought.
That is why your .030" patches are failing to seal - they are too thin for the tiny .520" ball- but might work with a .535" ball, which is already 12" smaller than the bore. The accuracy in the targets actually shows this.
With a larger ball, the accuracy will improve - but - you must learn to load it.
Here are different methods of loading- especially with the side by side. note it was loaded with a .562" ball and .0215" patch. I switched to using a .574" ball and a .0235" patch and loading was virtually identical. To the rest, sorry for yet again, posting these videos.
.45" pure lead ball, 10 ounce denim patch that I measured at .0225". The barrel had been loaded and fired approximately 50 or 55 times that day and had not been wiped at any time - just loaded and fired as we do. No patches burn and if picked up, could easily be reloaded and shot again. They are not scorched, either and are still dam.
Note- Ross is shooting a smoothbore with round ball and a fairly snug patch. It actually loaded no quicker than the rifle.
This is me with my .58 Kodiak and the undersized .562" pure lead balls in a .580" bore with .008" rifling depth.
lastly, this is brother Taylor shooting his .50 Virginia rifle with a .490" ball and .022" denim patch. The rifling in this gun is .016" deep and with over 85gr. of powder, it will start to scorch the patches in some grooves, causing flyers. This rifle needs a .495" ball, which I believe Taylor adopted after this experiment.
None of these guns EVER needs wiping during a day's shooting.