From what you measured, the rifling bore is very close to a .28 caliber. With the narrow rifling the photo shows, your .280 measurement was probably pretty good.
The angle on the rifling on the slug looks like the rate of twist is very slow. That indicates the gun was most likely made for shooting cloth patched lead roundballs. Normally, a patched lead ball size is approximately .010 smaller than the bore. That would mean the gun would shoot a .270 diameter ball.
Now for the bad news. I checked the Track of the Wolf's web site and the smallest lead ball they offer for sale is .283 in diameter.
https://www.trackofthewolf.com/List/Item.aspx/127/1
Although you could drive that size ball down the bore if you used a hammer, it wouldn't shoot very well. The ball needs the cloth patch to not only grab the rifling but to also seal the grooves off by making a tight seal.
Dixie Gun Works catalog shows a "Tatham's Compressed Buck Shot and Lead Balls chart that says that somewhere there is a No. 2C buckshot that is .270 in diameter and that would work if you could find it. It is also called "IV" in Germany. That 2C is not to be confused with "#2 American standard shot" though. #2 shot is .150 in diameter so it wouldn't work.
I'm going to move this thread to the General Muzzleloading area because the question applies to all muzzleloading rifles.