May I add a couple of ideas to the mix? The first is that you can simply drop your barrels in warm to slightly hot water, before you start any work, and find out if you have any voids in the rib solder. The heat will expand the air between the ribs and create bubbles. I do this before starting any rust bluing project so as not to get any surprises later. You can then add a small hole near the forend lump, which in most cases will allow any water to leave. Removing the front bead will help this. When you remove the barrels from the boil, allow the water to drain, then tightly twist a small piece of paper towel and insert it in the hole. This will wick away any remaining water.
Another thing is that Laurel Mt. will indeed give you a copper color if applied thickly or twice, but this will still rust properly if your heat and humidity are correct. The end product, to my experience, is no different. Also, LM can be dilluted so as not to give such a course finish if desired.
Based on your pictures, it's the ribs weeping, not any copper deposits, causing the issue.
Last but not least. If the ribs are weeping, there is a problem, and it could be a very unpleasant one. A small hole or two may simply be a bad original soldering job. More than that and you've got rust issues between the ribs.
Luck,
Jim
