Ocean acoustic tomography (OAT) methods aim at estimating variations of sound speed profiles (SSP) based on acoustic measurements between multiple source-receiver pairs (e.g., eigenray travel times). This study investigates the estimation of range-dependent SSPs in the upper ocean over short ranges (<5 km) using the classical ray-based OAT formulation as well as iterative or adaptive OAT formulations (i.e., when the sources and receivers configuration can evolve across successive iterations of this inverse problem). A regional ocean circulation model for the DeSoto Canyon in the Gulf of Mexico is used to simulate three-dimensional sound speed variations spanning a month-long period, which exhibits significant submesoscale variability of variable intensity. OAT performance is investigated in this simulated environment in terms of (1) the selected source-receivers configuration and effective ray coverage, (2) the selected OAT estimator formulations, linearized forward model accuracy, and the parameterization of the expected SSP variability in terms of empirical orthogonal functions, and (3) the duration over which the OAT inversion is performed. Practical implications for the design of future OAT experiments for monitoring submesoscale variability in the upper ocean with moving autonomous platforms are discussed.