Wind farm flow control has demonstrated significant potential to increase wind farm power and energy production. Two commonly used methods are wake steering, which entails yaw misaligning individual turbines to deflect wakes laterally, and induction control, which typically modifies the thrust coefficients of individual wind turbines to reduce wake deficits. These two control approaches are often studied and utilized independently. This study investigates the combination of both of these strategies, termed <em>joint yaw-induction control</em>. By synergistically controlling wind turbine yaw angles and thrust levels, increased wind power can be achieved compared to either induction or yaw control in isolation. This research leverages the Unified Momentum Model to capitalize on the interplay between the yaw misalignment and the thrust coefficient of a turbine rotor on the power and wake velocities generated by the wind turbine. The Unified Momentum Model is integrated with blade element modeling to yield a blade element momentum model that both predicts the power and forces on wind turbines with arbitrary input of yaw, pitch, and tip speed ratio, and also predicts the initial wake velocities needed for far-wake models. Forward-mode automatic differentiation is integrated into the rotor and wake model to efficiently optimize control strategies using gradient-based optimization. Using the fast-running wind farm model, which is a coupling between the Unified Momentum Model and a Gaussian far-wake model, we demonstrate that joint yaw-induction control outperforms individual yaw or thrust control strategies, leading to significant increases in power production. First using a two-turbine test case, we show that the Unified Momentum Model reliably predicts the dependence of the freestream turbine power on its yaw and thrust coefficient compared to 210 independent large eddy simulations of wind turbines in a conventionally neutral atmospheric boundary layer. However, larger discrepancies result from the wake model, particularly in yawed conditions. The leading turbine control strategy that maximizes the combined power of the two turbines entails yaw misalignment and a thrust coefficient larger than Betz-optimal. Next, a 25-turbine wind farm case study highlights the benefits of integrated rotor and wake modeling but indicates that improvements in fast-running, gradient-compatible wake models are required to realize the potential benefits of joint yaw-induction control. The findings underscore the importance of modeling interdependencies between yaw and induction control to inform effective optimization strategies.