Seaweed biomass presents a substantial opportunity for climate mitigation, yet to realize its potential, farming must be expanded to the expansive open oceans. However, in the open ocean neither anchored farming nor floating farms operating with powerful engines are economically viable. Recent studies have shown that vessels can navigate with low-power engines by going with the flow, utilizing minimal propulsion to strategically leverage beneficial ocean currents. In this work, we focus on low-power autonomous seaweed farms and design controllers that maximize seaweed growth by taking advantage of ocean currents. We first introduce a Dynamic Programming (DP) formulation to solve for the growth-optimal value function when the true currents are known. However, in reality only short-term imperfect forecasts with increasing uncertainty are available. Hence, we present three additional extensions. Firstly, we use frequent replanning to mitigate forecast errors. For that we compute the value function daily as new forecasts arrive, which also provides a feedback policy that is equivalent to replanning on the forecast at every time step. Second, to optimize for long-term growth, we extend the value function beyond the forecast horizon by estimating the expected future growth based on seasonal average currents. Lastly, we introduce a discounted finite-time DP formulation to account for the increasing uncertainty in future ocean current estimates. We empirically evaluate our approach with 30-day simulations of farms in realistic ocean conditions. Our method achieves 95.8% of the best possible growth using only 5-day forecasts. This confirms the feasibility of using low-power propulsion to operate autonomous farms in real-world conditions.