The problem with just welding is that you will either have a void on the inside where the weld didn't go right to the bore (this will collect fouling) or the weld will protrude into the bore that make it difficult to clean right to the breech if left and be a gripe to file out. However, if you want to weld it, make your plug screw short, half as long as the wall thickness of the barrel, run it in until it is flush with the bore, mark it (inside the bore) remove it and file the end to match the contour of the bore interior. Then reinstall the screw, and weld up the remaining hole and file flush. The hole should be countersunk to the depth of the screw so you get a good solid weld right to, and penetrating into the screw. Then just clean up the inside with a round file to ensure there's nothing will snag a cleaning patch. This will only be viable if you intend to leave the barrel in the white. If you intend to blue or brown it, the weld will almost certainly color differently from the rest of the barrel and will not look good at all. If you just use a plug, leave the plug just a shade above the surface of the barrel and peen it before fileing it flush. This will give an invisible joint and the screw MIGHT color the same as the barrel. If not, at least it will be a nice round discoloration rather than a blob shaped thing that the weld will leave.
Cody
PS I don't know the weldability of 12L14. As previously suggested, it may not weld well.