> Floating trees in the open ocean.

The more refined version of this are intentionally created algal blooms, ala the red tide. Then you would somehow capture the CO2 dissolved in ocean water that the algae concentrates.

In this way you'd use the ocean itself as your carbon capture "filter" and "clean the filter".

The issue is that since there just isn't enough nutrients for life, and adding fertilizers costs more carbon than it sequesters. The deep ocean usually gets its nitrogen from life dying above, decaying downwards then getting pushed upwards again. I don't know of any deep ocean reserves of nitrogen that just needs brought to the surface.