Dynamic Soil-Structure-Interaction (SSI) significantly influences wave propagation in the ground, motivating the development of computationally efficient methods for accurately predicting ground-borne vibrations and assessing the performance of mitigation measures. In this contribution, a three-dimensional coupled Integral Transform Method (ITM)-Finite Element Method (FEM) framework for modeling a metabarrier consisting of resonator arrays embedded in a linear elastic stratified half-space is presented. The modeling objective is achieved by the superposition of two analytically solvable subproblems: a half-space and a spherical cavity embedded in a full-space, while the metabarrier is modeled by finite elements which are coupled at the spherical outer boundary. Two alternative ITM formulations are compared. In the original formulation, the half-space is described in Cartesian coordinates and solved using a twofold Fourier transform, while the cavity is solved via a Fourier-Legendre series expansion. This formulation leads to elaborate wavenumber coupling, as all Cartesian wavenumbers of the half-space solution must be considered together with the angular wavenumbers of the cavity solution. The proposed formulation describes the half-space in cylindrical coordinates and solves it using a Fourier series expansion in the azimuthal direction and a Hankel transform in the radial direction, while retaining the cavity solution. Thus, the azimuthal wavenumbers of both subproblems can be coupled directly, enabling a parallelized implementation and the efficient treatment of layered soil configurations. Amplitude reduction factors are evaluated using both formulations, and the mitigation effectiveness of the metabarrier is compared in homogeneous and stratified soil. The results demonstrate that while both formulations capture the SSI, the parallelized formulation significantly reduces computational cost and eliminates numerical artifacts arising from the periodic ansatz functions in the original formulation.