Cleaning Solder 'Burns'

I am soldering bezel cups (silver, probably - the generic kind) to
stainless. I am using a silver solder, and Rio Grande’s pink
Solder-Fast for Gold & Silver flux. [which turns white and bubbly
when heated, although I was assured that it was the stuff that turns
pitch black when heated]. I have the steel polished to a
mirror-shine prior to doing any work. I flux the bezel, heat solder
onto it, flux it again and press it to the steel - trying to make
sure no flux (liquid) spills all over. Then I am heating the steel
from behind to get it to tempurature without liquifying the bezel.
Invariarably it either doesn’t stick well, or it does but leaves a
nasty black burn around the bezel (in addition to the heat
coloration.) The heat coloration buffs right off with yellow-gold
rouge, returning that section to a mirror. However, right around
the bezel I have that nast black stuff that seems like caked on,
burnt on stain. It doesn’t buff off, and I am afraid to sand or
grind that close to the bezel.

Anyone have a quick/easy/effective way to remove that black stuff?
I refuse to pickle the stuff, if possible, as that normally pits the
surface of the metal and sets me 5-6 hours back on post-solder
polishing. I already have a mirror on the surface, and would like
to have to grind as little as possible after the torch-work…

Thanks,
Russ