Try the "colour key" video effect applied to the Fireworks clip, with black as the selected colour (use the dropper as the black probably isn't as black as you think!)
Thanks Matt for your time and excellent answer.
Two things that I would think about doing would be using Keyframes to animate the fixed Effects Motion>Scale and Motion>Position. Also, Opacity. With a large enough "dark field" you can also combine the displays at different sizes and locations. Depending on what is in your original footage, you could even super these over say a skyline shot. You might have to use the Garbage Matte to remove foreground, or background material from your fireworks, but should be able to get things looking very good.
Also check out the Remove Matte effect (set to black) that's built into Premiere. You might also have success with the free Unmult plugin from Red Giant. You might have to drop a Levels or Curves effect before these in the effects stack to make the black "more black," as Matt suggested.
Perhaps even easier, with your fireworks clip stacked above your background in your sequence, swivel down the clip's fixed Opacity effect, and change the blending mode to Screen or Linear Dodge (Add). Many times, this will easily punch out the black in a clip and allow you to superimpose the non-black pixels on a background. Again, a levels change can help to clean up the background before supering the image.