I'm thinkin' two things. One, continue to clean it out until you get good metal to solder to, fill it and let it be. Two, if the spot is relatively round, drill it out all the way through, countersink, and rivet in a bit of brass rod and peen it all in place. Other than the color, this would make a more invisible fix.
If you could make a "rivet" from a bit of the same brass as the plate, that would be great. Maybe you could find an old buttplate or something lying around that the color matches up pretty well on, and use it to make a rivet out of.
I don't know about you, but I have a dresser drawer full of buttplates and triggerguards!