Middle barrel bulge is most likely from a bullet having got stuck in the barrel from underloading or failure of contaminated powder to burn completely, then a second round with good powder being fired into it rom behind. If the bulge is extremely slight and you think it may be a manufacturing error in making the exterior contour, slug the barrel with a pure lead bullet or ball. If the friction against the slug is uninterrupted as it pases under the bulge, you are in good shape. If the bulge resulted from an "incident", then you will feel the slug get very loose in the bore when it passes through the bulged portion. In this case you would not only need to replace the barrel assembly, but also check the frame for distortion and chamber dimensions to be sure it didn't bulge the chamber that fired the last round.
A barrel with a bulge in it should shoot blanks, but no real ammunition should be put through. Even if you did put it through, it would tend to lead in the bulged area and wouldn't likely be very accurate. I have no idea whether any replica exists that would have compatible replacement parts available? If not, then you need to look at blanks or take Harry's suggestion.
Nick