Driving a slug with a wooden dowel is just asking for trouble. You are so lucky you did not cause an obstruction that would be very hard to remove. Wood has no place inside a barrel. I would use a close fitting flat nosed steel rod wrapped with tape every couple of inches to protect the bore.
That being said I would never slug a barrel because I had an accuracy problem. If you managed to successfully drive a slug through the barrel (breech to muzzle) and got an accurate slug to examine, how and what would you do next? You may be able to accurately measure the diameter (bottom of the grooves)? Are you able to measure the bore? (Top of the rifling). And what would that tell you?
Slugging a bore is usually done to determine exact size to determine what you need for shooting lead bullets most accurately.
Quite possibly enough was not removed from the muzzle of the barrel when it was installed.