Conjecture on non-defectivity for degrees at least $(3,3)$

Let $\mathbf{n}=(m,n)\in\mathbb{N}^2$ and $\mathbf{a}=(a,b)\in\mathbb{N}^2$, and let $X_{\mathbf{n},\mathbf{a}}$ be the two-factor Segre-Veronese variety associated with these parameters. Assume that $\mathbf{a}\geq(3,3)$ coordinatewise.

Non-defectivity conjecture for degrees at least $(3,3)$. There are no defective two-factor Segre-Veronese varieties $X_{\mathbf{n},\mathbf{a}}$ for any $\mathbf{n}\in\mathbb{N}^2$.

This is a weaker consequence suggested by the paper's broader classification conjecture. The paper gives computational evidence and known results supporting it, but does not establish the claim in full.