Success! Steel wool in the freshly-dirtied pickle worked like a charm, and now my copper filigree star is all copper-colored. I threw it in the tumbler again to shine it up, and it's now adorning the top of my silver, fiberoptic studio Xmas tree.
I also designed a basic approach to doing a filigree snowflake- which I think is a nifty idea!- and have started work on it. The filigree wire I'd made was just exactly long enough for all the component pieces, so I think that's a good omen!
I'm still thinking about other ways to use this. I like the idea of it edging a Victorian-style brooch, for instance, plus the use of it for hair ornaments sounds very rich in potential. I'll be getting more wire to enable lots of experimentation...
Perhaps this will be a consistent "theme" that would make my work more functional in gallery sorts of environments! Or maybe not. :)