I'm wondering about particle size too! Molten blobs that sparkle sounds like a poorly milled attempt at BP too!
I find the charcoal has to be very fine for a good effect. I specifically tried coarser charcoal assuming it's microstructure might be important, especially in producing the dividing sparks, but found that actually killed the effect. This may be why some lampblacks work well. Surface area may be important, I've noted that the dross balls shot out from the main dross ball get brighter and pulse in diameter just before they explode. I did this by careful examination of long exposure photography of senko hanabi. I strongly suspect internally generated gasses blow the droplets apart and the subdroplets continue to react In the same way until they run out of chemicals or cool off. It is probably important that there is plenty of fine charcoal in suspension in the melt to continue the reaction down in the daughter droplets to get the most lacey effect.
I wonder what the gas bubbles are? Carbon dioxide from sulfate oxidizing the charcoal? The role of volatile compounds in the charcoal might be worth study. I've tried replacing the charcoal with organic compounds like sugar and benzoates with no luck, it may be that charcoal has just the right reactivity.