Generalized $q$-Gaussian von Neumann algebras with coefficients, III. Unique prime factorization results

We prove some unique prime factorization results for tensor products of type $I{I}_1$ factors of the form ${\mathrm{\Gamma }}_q(\mathbb{C},S\otimes H)$ arising from symmetric independent copies with sub-exponential dimensions of the spaces $D_k(S)$ and dim$(H)$ finite and greater than a constant depending on $q$.