I went through that decision recently when I finally decided to finish my 1803 Harper's Ferry. Mine is the Track of the Wolf Special Project Parts Kit (Translation: Rifle Shoppe). ToW now has their own kit. Back to the under rib.
The real problem is the fact that the barrel is round. There was no good way to clamp the rib to the round barrel for soldering. Most previous experience was attaching a rib to the bottom flat of an octagon barrel. Measuring the thickness of the barrel wall showed that we had enough thickness to get three threads in a 6-48 thread. Next 5 screws were turned and threaded. The top slot was left high to use to turn in the screw. The thimbles were placed on the rib and five locations were marked for the screws. The rib was drilled with the tap sized drill. The barrel was installed in the mill and the lowest point was determined and the first hole was located, drilled and tapped. The hole in the rib was opened to the screw body and the rib was now located by that screw. The other four holes were worked the same way. The rib, thimbles were polished and the screws were tightened. The rib looked good and on the bottom. Locktite red was put on the threads of the screws and tightened down. The screw heads were filed off and peened to fill any gaps. Riveting would work about the same way and would probably be quicker.
