This article presents a new analysis and design for the dynamic positioning of remotely operated vessel using the state-dependent Riccati equation (SDRE) scheme. The focus is on the computational performance for efficient communication. The novel analysis completely removes the dominant routine (applicability/solvability check) at each time instant or system state, which differs from the common numerical compromise that is subject to limited states and precision. The design framework also facilitates the analysis of the α-parameterization technique, which is a usual practice (built on empirical confidence) but, actually, cannot guarantee alleviation of computational burden. The finding, in a unified manner, clarifies whether the practice is effective with respect to the associated eight degrees of freedom, which separate into two respective groups by virtue of a simple condition with reduced dimensionality. At those newly discovered system states corresponding to unsolvable SDREs, we alternatively introduce a solution to construct feasible state-dependent coefficients (SDCs), and maximize/unify its general capability with a proof and a MATLAB® implementation. From a practical viewpoint, numerical experiments also validate the proposed combined scheme, which entails (i) computationally enhanced classical SDC construction with verification and (ii) an efficient alternative. Finally, we demonstrate the impact within and beyond this marine system.