  Given a solution $Y$ to a rough differential equation (RDE), a recent result
[8] extends the classical It\"{o}-Stratonovich formula and provides a
closed-form expression for $\int Y \circ \mathrm{d} \mathbf{X} - \int Y \,
\mathrm{d} X$, i.e. the difference between the rough and Skorohod integrals of
$Y$ with respect to $X$, where $X$ is a Gaussian process with finite
$p$-variation less than 3. In this paper, we extend this result to Gaussian
processes with finite $p$-variation such that $3 \leq p < 4$. The constraint
this time is that we restrict ourselves to Volterra Gaussian processes with
kernels satisfying a natural condition, which however still allows the result
to encompass many standard examples, including fractional Brownian motion with
$H > \frac{1}{4}$. Analogously to [8], we first show that the Riemann-sum
approximants of the Skorohod integral converge in $L^2(\Omega)$ by adopting a
suitable characterization of the Cameron-Martin norm, before appending the
approximants with higher-level compensation terms without altering the limit.
Lastly, the formula is obtained after a re-balancing of terms, and we also show
how to recover the standard It\"{o} formulas in the case where the vector
fields of the RDE governing $Y$ are commutative.
