What sort of tool or process is used to clean the excess solder from the exterior edge of the seams?

Ruff Hunter, I have always used a very sharp chisel first to cut out any big lumps of the solder. I use it with the beveled side toward the metal, less chance of gouging into the bbl or rib that way. Then use the end of a file that I grind a bevel on so that it will get as mugh into the joint as possible. Make the end of the file look like a chisel. You are actually "draw" filing with the end of the file, cutting "cross-ways" with the teeth rather than useing the file in the normal length-wise motion. Keep cleaning the file with a file card and rub chalk on the file teeth to help keep it from "piping". If still is a line of solder you can usually scrape away the last bit with utility knif blades by hand. The ones I use are Stanley Industrial quality, they hold the edge better than any I have used. Assume you are going to reblue, so then you can "sand-blast" the joing, I use Aluminum Oxide 80 grit media at about 60 psi in my cabinet, then complete with the wet/dry sandpaper. Hope this gives you some ideas. Mabee Chuck will comment, I bet he has some good methods too.
Regards, John Hancock

Can you share what type flux you used? I understand an acid flux is best used with steel, but it bad when not neutralized between the barrels.