Lube the bore before you try to pull it again, if you didn't the first time. I haven't seen this mentioned, and in the heat of the frustration, things can be overlooked.
Once you get it moving it should come right on out. If you've drilled thru it, powder isn't going to move it, or grease, possibly air--but you'd need a bigger hole on the backside than a drilled touchhole. If you've drilled thru the ball, you need bigger threads as mentioned above. I don't know what is readily available but any hobby machinist or experienced tinkerer should be able to help you make something up to work with your equipment.
If you're comfortable taking the bbl out, and installing a touchhole liner--could drill and tap for such, then use a grease or air fitting to push it out (before fitting up your new liner). This could work with a thru-hole if you had big blasts of air--being mindful of what is "down range". Simply drilling for the liner could get into the ball, and provide enough access to manually get it moving or carve on it and peel it out.
If you're not comfortable disassembling the gun, find someone who is--not the first jasper who thinks he is, but someone who has built a M/L or two.
Enjoy the process as it gives you lots of ways to remember to -not- re-visit this whole process. Best of luck.