Nice effect! Can we see the cap, I'm curious to how you got such a cartoony cell shaded look to the effect.
I think you can achieve everything in that Explogen program if you just use an animated sprites and generate about 200 of them..looks like simple kind of fireworks physics...the 'fussy' modes look like they are just 'additive'.
Particle object clearly needs an 'initial speed randomization' and perhaps a mode to render each particle with additive (achieved with render states, so no slowdown)