Let $\mathfrak g$ be either the Lie superalgebra $\mathfrak{ gl}(V)\oplus\mathfrak{ gl}(V)$ where $V:=\mathbb C^{ m|n}$ or the Lie superalgebra $\mathfrak{ gl}(V)$ where $V:=\mathbb C^{ m|2n}$. Furthermore, let $W$ be the $\mathfrak g$-module defined by $W:=V\otimes V^*$ in the former case and $W:=\mathcal S^2(V)$ in the latter case. Associated to $(\mathfrak g,W)$ there exists a distinguished basis of Capelli operators $\left\{ D^\lambda\right\}_{ \lambda\in\Omega}$, naturally indexed by a set of hook partitions $\Omega$, for the subalgebra of $\mathfrak g$-invariants in the superalgebra $\mathcal{ PD}(W)$ of superdifferential operators on $W$. Let $\mathfrak b$ be a Borel subalgebra of $\mathfrak g$. We compute eigenvalues of the $D^\lambda$ on the irreducible $\mathfrak g$-submodules of $\mathcal{ P}(W)$ and obtain them explicitly as the evaluation of the interpolation super Jack polynomials of Sergeev--Veselov at suitable affine functions of the $\mathfrak b$-highest weight. While the former case is straightforward, the latter is significantly more complex. This generalizes a result by Sahi, Salmasian and Serganova for these cases, where such formulas were given for a fixed choice of Borel subalgebra.
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