Conjecture on explicitness of categorical quotients and invariant rings

Let $K$ be an algebraically closed field of characteristic zero, let $G$ be a connected reductive algebraic group of the form $cprod G_i$, with each factor a torus or a classical simple algebraic group, and let $V$ be a rational representation specified by the tuple in the source. Write $V/G=\operatorname{Spec}(K[V]^G)$ for the categorical quotient, and let $V_\lambda(G)$ denote the irreducible Weyl modules occurring in $V$. Explicit quotient conjecture. The categorical quotient $V/G$ is explicit in a relaxed sense in general, without restriction on $m$. It is strongly explicit if $G$ is a product of classical simple algebraic groups and each $V_\lambda(G)$ is a subrepresentation of the tensor product of a constant number of standard representations of $G$ or their duals. The claim is intended to provide explicit invariant-theoretic data and an explicit FFT; the source gives no resolution.