... Why would you assume the jelly juice would weaken the explosion? I assumed quite the opposite - they used high explosives to put out the Kuwaiti oil well fires (basically the idea is the explosion rapidly deprives the fuel for the fire while simultaneously creating a brief oxygen vacuum in it's explosive cavitation [which also provides some measure of cooling], basically knocking out all three sides of the fire triangle in one go). While I wouldn't class the JJ as a high explosive, even mid range force-per-kilo explosives can be used to put out fires (ask any redneck who's thrown a rusty propane tank in a bonfire... Assuming it didn't go missile).
So yeah, as for the original idea that the fireball is kind of like Quote's cigar lighter for the bomb, I kinda doubt that. I'd personally say that the bomb had a timer and detonator (looks like it on the sprite, and if it *doesn't*, Malco is a terrible bomb maker), which means the fireball really isn't key to the story, unless of course it's kinda like Santa and Chaco's "hey, this guy's cool, let him pass" code item.
Also, I wouldn't say any weapon is really story-centric. I mean, every weapon is given to you to counter obstacles you may encounter (Polar Star for breakable blocks and the Door, Missile Launcher for the first/"second" boss, Fireball to help with Grasstown's rolling slopes, MG to help with the Sandzone's treacherous floor, Blade to deal with greater enemy health, and the upgraded missiles to deal with the impending bosses. As for the Snake, Whimsical Star (I consider it a weapon!), Spur and Nemmy, those are kinda like... "Hey, those guns are cool, but here's a weapon that may or may not suit your playstyle better". Also, well, Bubbler is kinda the Easter egg weapon of the game, IMO. Definitely helps in the Sandzone and with the Balfrog fight, though.)
... Just my two cents.