The SPH method is expected to be widely applicable due to improvements in accuracy achieved through Particle Shifting Techniques (PSTs) and high-accuracy approximation models such as SPH(2). However, the computational cost remains a practical issue. Recent studies have focused on parallelization techniques (e.g., Message Passing Interface (MPI) and Graphics Processing Units (GPUs)) and improved iterative methods for nonlinear differential equations to increase computational efficiency. Nonetheless, high computational costs continue to pose significant challenges because the particle size in the conventional particle methods must be uniform across the domain, and a considerable number of particles are needed to achieve sufficient accuracy and to apply the method to a wide range of simulations. Shibata et al. proposed an ellipsoidal particle method that reduces computational costs by introducing a coordinate transformation to change the aspect ratio of particles used in the MPS method, demonstrating the applicability of coordinate transformations to particle methods. In this study, we generalize Vertical Coordinate Transportations (VCTs) including an ellipsoidal particle method. In addition, we propose three novel methods with VCT, inspired by the body-fitted coordinate system in finite-difference methods and the σ-coordinate system used in the Princeton Ocean Model (POM), aiming to improve computational efficiency. The efficiency and accuracy of the proposed method are validated in a hydrostatic pressure problem. As a result, the combination of vertical coordinate transformation and the high-accuracy approximation model SPH(2) demonstrates its ability to achieve both accuracy and efficiency. Additionally, we confirm that volume conservation is satisfied by PSTs in a dynamic problem even in σ-SPH using a σ-coordinate system, where particle volume changes .