So, was there a better way to wick off this solder? Just asking
for future oopsies.
Nope. If you've got excess solder, stop heating, so it doesn't flow
beyond where you want. The remove the excess mechanically (files,
abrasives, gravers, etc.) Continued heating just lets the solder
penetrate further into the metal. You CAN remove enough of the solder
in many cases, that you'll be back to clean metal, and can again use
LOS for a finish. But you might have to do a bit of work to get
there, including perhaps removing the LOS, taking off a bit more
metal where it's revealed that there are still problems, and redoing
the patina again... Wicking off excess solder is a method used with
tin/lead electronics solders on circuit boards and the like, made
possible simply because the solder melts at such a very much lower
temperature than the items being joined, and simple copper wire braid
will soak up excess. There isn't an equivalent and equally effective
method with high temperature solders. As you've found, one just
usually makes more of a mess.
By the way, scotch stones, also known as "water of ayre", I think,
stones, are a naturally mined slate like stone that's sold as an
abrasive material. Very fine grained, used with water, it is
wonderful for cleaning up things like this without making even more
of a problem with the metal. Allcraft in new york carries them. they
were unavailable for some time, when the Scottish factory burned
down, but apparently are once again available in limited quantities.
Other abrasives, of course, are also available, but the scotch stones
are one of the traditional fixes for this type of cleanup problem,
and they work very well.