I hope you're still with me.
I would guess that the four of you, not including Bergthora, weigh around 800 lbs. This provides a near-guarantee of your safety; odds are about 1 in 450 that the rope would break, dropping you fifty feet for 15d6 damage.
You have every reason to believe you're perfectly fine. But I do want to give the sense of discomfort you ought to feel as the rope strains and creaks, as the cage descends. I also want to emphasize that the waters, viewed from 30 feet above, could easily conceal any number of creatures, things too small to be seen, flat things hiding in the water, things simply hiding in the dark. I don't want this to be discarded as a possibility. It would take 20 rounds for the cage to make a round trip from the bottom, where it let off half the party, to bring reinforcements.
But, let's take stock.
Can I count on the four of you going down together? Are you fine with Bergthora making a trip as a solitary person. She's fine with that.
If you're carrying your lanterns, you won't need to make a pot of fire for the cage. Your legs would blot out most of the light it would give out anyway. Petar and Willa have six torches between them, enough for two hours light, so you don't have to leave a lantern behind; you can take both of them.
What else needs to be discussed?