I have unplugged a similar plug. Actually, I've done it a couple of times.
The method I would recommend for this situation (relatively large bore, long obstruction) is to make a simple cutter out of soft metal (brass) and hand rotate it to slowly remove the bulk of the obstruction.
Take a piece of brass round stock a little under bored diameter (maybe .350) and file one end until it looks like a flat tip screwdriver tip, keeping the cutting part short (maybe 1/8") You could get fancy with undercuts or even make a "plus" shape for 4 cutting edges, but it'll all work about the same.
Lube up the sides, stick it in the bore, twist it a half dozen times, pull it out, tip the muzzle down and spray out the chunks of lead with wd40. It will take a long time to get through, but it will work.
I once had to do a .22 that had 16 projectiles stacked up (flobert BBcaps) and I just sat in front of the TV and whittled away at it, it took a couple of three hours IIRC.
Alternatively you could make a couple of collars for a commercial reamer, but IMHO this is riskier as if it goes cockeyed you could easily damage your barrel.
I think you have a very good chance your barrel is undamaged due to the very low pressure, just clean it out and look for "rings"
If you need help coming up with a brass hand reamer I can lathe one up for you easily enough.