Bacteria then shift to using sulfate as the terminal electron receptor and generate H2S.

There is a lot of sulfate in sea water, many orders of magnitude more sulfate than there is O2.

The problem of fresh water on the surface relates more to the circulation of arctic water around the world. The only reason the deep ocean is cold and has a lot of O2 is because cold and salty water from the arctic has a lot of O2 and sinks and then flows all around the Earth. If that flow stopped, because the cold fresh water at the arctic didn’t have a high enough density, then the flow stops and the thermal gradient (cold at the bottom) stops. That means the bottom heats up due to geothermal heat.

A reason that the organic matter from primary production doesn’t decompose as it sinks is because the deep water is colder than the surface water (where the bacteria that feed on primary production are). If there was no temperature gradient from the arctic circulation, then (I presume), sinking primary production carbon would be oxidized by bacteria as it sank, either by O2 (making the deep ocean anoxic), or by sulfate (making the ocean sulfidic).