Multibody dynamics research has enabled efficient and effective simulation, design optimization, control, and identification of mechanical systems, contributing significantly to applications as diverse as simulation-driven and optimization-based engineering design, robotics, digital-twin technology, and many more. Nowadays, different formulations are in use and their properties and comparative differences are especially well understood for numerical simulation purposes. Also, software for multibody modeling often predominantly takes simulation applications into focus. However, efficiency is particularly paramount when using multibody system (MBS) models for model-based real-time control, where, in particular, model predictive control (MPC) comes to mind. This contribution investigates different ways of discretizing the higher-index differential-algebraic equations (DAEs) of motion of an MBS model when implementing the MPC's underlying optimal control problem (OCP). In contrast to the widely used reduction to an index-1 DAE in combination with an implicit integration scheme, more direct approaches are proposed, exploiting the ability of nonlinear programming solvers to efficiently handle equality constraints. The proposed OCP implementations are evaluated on a set of example MBS, revealing a superior numerical efficiency, especially with state-of-the-art structure exploiting OCP solvers. The presented approaches are chosen so that they introduce as few additional hyperparameters as possible while allowing as much flexibility as possible in OCP design, and, this way, the obtained results demonstrate that the automatic synthesis of real-time capable MPC controllers from MBS models can nowadays be feasible without arduous per-system tuning or overly specific or limited numerical approaches. However, it is also noted that a prospective, automated workflow from MBS model to MPC controller poses certain requirements for multibody modeling software, motivating a discussion of how such software should be designed to facilitate optimal control, revealing desirable characteristics exceeding what is required for simulation purposes.