I hate to add to this because the Darwin Awards are much more fun when you know some of the contestants - LOL
A simple and safe way is to get a wooden dowel rod from the hardware store, 1/4" for a 300wm. Cut the rod to just over barrel length to eliminate as much flex as possible.
Next, take one or two cleaning patches (whatever fits) over the end of the rod and insert into the barrel all the way to the obstruction, now tap on the exposed end of the dowel rod (that's tap, not pound). Some pencil marks on the exposed dowel rod can indicate progress. With the bolt removed, tap away. The wood won't hurt the bore.
Good Luck
Southpaw