Some years back, I was in the same situation. No powder and the ball was firmly lodged at the breech of my Derringer rifle. First ball puller stripped out. No problem as I rummaged through my selection of double ended bangers (machine threaded on one end and wood threaded on the other). I have the 8, 10 , and 12 and I stripped them all out. At this time all I could get with the compressed air was a rush of air out the muzzle. Since I had the hole through the ball I knew that the grease pump solution was not the one to employ. The rifle was one I had built and breeched, so I had the wrenches to properly remove the breech and the heavy rod to drive the offending ball out.
When I posted my problem and solution, I got all the above arguments against pulling the breech plug. I do agree that pulling the breech plug is the last option to choose. The rifle in question, a Lyman Deerstalker, will have a breech plug installed to a level that most mere mortals will not be able to budge. A batter vise with formed jaws to hold but not damage the barrel is required. A large wrench that fits the breech plug a d a long cheater bar will be needed to remove and replace the breech plug. If the OP takes his rifle to have the plug removed, it should be to a black powder gunsmith.
Since the ball has been moved back to the breech and if the latest round of powder in the breech to shoot it out fails, then it would be time to screw the ball puller into the ball, use application of high pressure air or get the grease gun to use the pressure from the grease gun to remove the ball.
Lessons learned:
1. I should have tried feeding powder through the vent to shoot the ball out. My first choice with percussion guns is to shoot the ball out. Since I built the rifle, I knew how little space was behind the ball and I didn't have confidence with that method in a flint lock.
2. I should have drilled a pilot hole in the ball to prevent the ball pulling screw from expanding the ball and locking it in the barrel.