Call me crazy, but I think I found a method to get the cores to drop:

I was killing all the elementals and got three in a row, then nothing for 20 kills.

So I thought, "What if I alternate Sea Sprays and Sea Elementals?"

Sure enough, EVERY single kill by this alternating method resulted in a drop.  All 7 in a row.

I think that's statistically impossible to happen by pure chance.