Freeness conjecture for generic twisted quasi-invariants

Let $m$ be a nonnegative integer, let $f_1,f_2,\dots,f_n$ be one-variable meromorphic functions, and let $Q_m(f_1,\dots,f_n)$ be the space of polynomials $F\in\mathbb C[x_1,\dots,x_n]$ such that

$$\frac{(1-s_{i,j})\left(f_1(x_1)\cdots f_n(x_n)F(x_1,\dots,x_n)\right)}{(x_i-x_j)^{2m+1}}$$

is smooth on the domain where the product $f_1(x_1)\cdots f_n(x_n)$ and its inverse are smooth, for all $1\le i<j\le n$. Generic twisted-freeness conjecture. For generic $f_1,\dots,f_n$, in particular when $f_i/f_j$ is not a monomial in $x_1,\dots,x_n$, $Q_m(f_1,\dots,f_n)$ is a free module over the ring of symmetric polynomials in $x_1,\dots,x_n$. This generalizes the known monomial-twist setting, but freeness in the generic case remains open.