Why did my reverse spherification method fail to produce proper spheres?
I don't have direct experience of this concept, but I do have a couple of comments that might help.

A general comment about your choice of calcium salt: 

Gluconates have a side effect - they numb mouth tissue (like taste buds). It is not a drastic effect, but that is why gluconates are the salts of choice for that stuff you put on mouth ulcers ...

I just don't like the idea of eating calcium chloride - I think I would prefer calcium acetate, if you can get it.

About the alginate bath - if the globules eventually sank to the bottom, you are fighting a surface effect, rather than having a density problem.

When I thought of ways to reduce the surface tension, I kept coming back to the idea of adding a little disodium phosphate to the alginate solution. That would also contribute to formation of globules, because it would form an insoluble complex phosphate with the calcium.

WTH, knowing my luck, adding disodium phosphate to the alginate solution could make the effect worse. I'm guessing ...

There is the consideration that, if there is calcium in your water, adding a little disodium phosphate the night before you use it will cause the calcium to precipitate and drop out of the water - then you can pour off the supernatant water, confident that the calcium is staying in the bottle.