Macroscopic superconductivity models have improved significantly over the last decades. Formulations and methods have been developed to faster solve problems involving high-temperature superconductors (HTS). Despite these developments, finite element analysis (FEA) of AC superconducting machines (SCMs) with HTS coils still remains time-consuming. The combined burden from the HTS models and the moving mesh makes the models complex and slow. To deal with this challenge, a new framework for FEA of AC superconducting SCMs with surface-mounted permanent magnet (PM) rotors and HTS armature windings is proposed in this paper. In this approach, the rotating rotor geometry is emulated with a stationary array of small PM segments excited with time-varying boundary sources. The major benefit of this approach is that the models can be realized without moving meshes, which increases the computation speed by more than one order of magnitude. In our dedicated case study of a complete SCM design, the speedup factors are 17.4x and 38.5x for the H-A and T-A formulations, respectively. Over a large parametric space of 18 design permutations, the highest relative error in calculated HTS loss was 4.12 percent. As a result, this work enables the designer to perform much more comprehensive performance studies of SCMs.