Continue with removing shards
Any pieces that cannot be readily pried out are removed with the soldering iron. One by one, and using only minimal flux, melt out the solder attaching the remaining shard to the rest of the piece. As you melt the solder, push down a bit on the piece to start dislodging it. Be careful not to damage the foil on the intact pieces of glass.

Replacement piece
Clean out the cavity with your soldering iron. Cut out your replacement piece, grind the edges and foil. Place a moist sponge under the cavity to support the piece at the correct height to insure your piece is level with the surface of the rest of the work. Flux, solder and restore patina.