Though he didn't think about the climatic effects, Arthur C. Clarke beat you to it by a couple of decades in The Deep Range. Not with sewer sludge, but he proposed fertilization and phytoplankton farming to feed the whales... (and there's more to it if you haven't ever read it. Though dated, it's still surprisingly prescient.
I'm not sure if the Pacific Gyre would work as well as the Southern Ocean. The Southern Ocean has plenty of nitrate and phosphate, but not enough iron, which is why iron fertilization works there. The Pacific Gyre doesn't have any upwelling, so it doesn't have nitrate, phosphate or iron (it's a long way from any continents in the mid-Pacific). Though sewer sludge would provide some nitrate and phosphate, and you could enrich it with a little bit of iron, the vast size of that oceanic region means that the scale of the amount you'd have to ship out there is really large.
I agree. These grant funded social scientists are playing at changing the climate to suit the political fashion of the day.
I have no doubt that the Earth will recover from any Woops! they create, but mankind might not survive to record the empirical datum.