Ensuring that global warming remains <2 °C requires rapid CO2 emissions reduction. Additionally, 100-900 gigatons CO2 must be removed from the atmosphere by 2100 using a portfolio of CO2 removal (CDR) methods. Ocean afforestation, CDR through basin-scale seaweed farming in the open ocean, is seen as a key component of the marine portfolio. Here, we analyse the CDR potential of recent re-occurring trans-basin belts of the floating seaweed Sargassum in the (sub)tropical North Atlantic as a natural analogue for ocean afforestation. We show that two biogeochemical feedbacks, nutrient reallocation and calcification by encrusting marine life, reduce the CDR efficacy of Sargassum by 20-100%. Atmospheric CO2 influx into the surface seawater, after CO2-fixation by Sargassum, takes 2.5-18 times longer than the CO2-deficient seawater remains in contact with the atmosphere, potentially hindering CDR verification. Furthermore, we estimate that increased ocean albedo, due to floating Sargassum, could influence climate radiative forcing more than Sargassum-CDR. Our analysis shows that multifaceted Earth-system feedbacks determine the efficacy of ocean afforestation.