Ratios conjecture for quadratic Dirichlet L-functions over function fields

Let $\mathcal{H}_{2g+1}$ be the set of monic square-free polynomials of degree $2g+1$ over $\mathbb{F}_q[x]$, and let $\mathbf{A}=\{\alpha_1,\ldots,\alpha_k\}$ and $\mathbf{B}=\{\beta_1,\ldots,\beta_k\}$. Assume

$$|\operatorname{Re}\alpha_j|<\frac14,\qquad \frac1g\ll\operatorname{Re}\beta_j<\frac14\qquad(1\leq j\leq k).$$

For $\mathbf{C}=\{\gamma_1,\ldots,\gamma_k\}$, write $\mathbf{C}^{-}=\{-\alpha:\alpha\in\mathbf{C}\}$ and $q^{-2g\mathbf{C}}=q^{-2g\sum_{j=1}^k\gamma_j}$, and define $\mathcal{S}_{\mathbf{C}}$ by the Euler-product expression in the conjecture below.

Ratios Conjecture. Under these constraints,

$$\frac{1}{|\mathcal{H}_{2g+1}|}\sum_{D\in\mathcal{H}_{2g+1}}\frac{\prod_{j=1}^kL(1/2+\alpha_j,\chi_D)}{\prod_{j=1}^kL(1/2+\beta_j,\chi_D)}\sim\sum_{\mathbf{R}\subset\mathbf{A}}q^{-2g\mathbf{R}}\mathcal{S}_{(\mathbf{A}\setminus\mathbf{R})\cup\mathbf{R}^{-}},$$

with some power-saving error term, where

$$\mathcal{S}_{\mathbf{C}}=\frac{\prod_{1\leq i\leq j\leq k}\zeta_q(1+\gamma_i+\gamma_j)\prod_{1\leq i<j\leq k}\zeta_q(1+\beta_i+\beta_j)}{\prod_{1\leq i,j\leq k}\zeta_q(1+\beta_i+\gamma_j)}$$ $$\times\prod_{P\in\mathcal{P}}\prod_{1\leq i\leq j\leq k}\left(1-\frac{1}{|P|^{1+\gamma_i+\gamma_j}}\right)\prod_{1\leq i<j\leq k}\left(1-\frac{1}{|P|^{1+\beta_i+\beta_j}}\right)\prod_{1\leq i,j\leq k}\left(1-\frac{1}{|P|^{1+\beta_i+\gamma_j}}\right)^{-1}$$ $$\times\prod_{P\in\mathcal{P}}\left(1+\left(1+\frac{1}{|P|}\right)^{-1}\sum_{i+j\geq2\ \mathrm{even}}\frac{\mu_{\mathbf{B}}(P^i)\tau_{\mathbf{C}}(P^j)}{|P|^{(i+j)/2}}\right).$$

The conjecture predicts an asymptotic formula for averages of ratios of products of quadratic Dirichlet $L$-functions over function fields, extending the ratios-conjecture framework to this family; the paper proves special cases, while the full formula remains conjectural in the stated generality.