Long story short, I was using a wooden dowel to push a patch through my 397 and about halfway down I accidentally broke it off. It was a clean flat snap so I just used the rest to continue until I managed to do it again. The patch was a little snug but not tight so I used the other piece to continue pushing through until I realized the two ends at one of the breaks were just separating and spreading out inside the barrel, and then it broke again flush with the muzzle.
Is there a way to get the wood out of there? I should have listened to my doubts about using a 0.125" piece of wood but it was the best way at the time to keep the rifling nice. There was a tiny amount of Hoppe's #9 bore cleaner on the patch, thinking I'd be able to send a couple dry ones through and oil right after it so hopefully it's not harming the brass