This study explores an alternate direct transcription strategy where moving finite elements are embedded within the solution of the optimization problem. The approach also requires a mesh refinement stage, but it contains two important features: direct determination of the break-point as part of the finite element mesh, and a stopping criterion based on the profile of the Hamiltonian function. The incorporation of moving finite elements also introduces a number of additional difficulties. Because a variable mesh introduces additional nonlinearity into the equality constraints, and therefore (additional) nonconvexity into the NLP formulation, we explore a decomposition strategy where the inner problem deals with a fixed mesh, and the outer problem adjusts the finite elements in the mesh based on a number of criteria. This two level approach leverages NLP sensitivity capabilities for the inner problem and allows for flexible problem formulations in the outer problem for mesh placement. As a result, it decomposes a difficult, poorly posed problem into two parts: a large-scale problem that is easier to solve, and a smaller, more difficult problem that can be tailored to specific problem classes and challenges. Several optimal examples are considered to demonstrate the effectiveness of this approach.