On the directed Oberwolfach problem for complete symmetric equipartite digraphs and uniform-length cycles

We examine the necessary and sufficient conditions for a complete symmetric equipartite digraph $K_{n\left[m\right]}^{*}$ with $n$ parts of size $m$ to admit a resolvable decomposition into directed cycles of length $t$. We show that the obvious necessary conditions are sufficient for $m,n,t\ge 2$ in each of the following four cases: (i) $m\left(n-1\right)$ is even; (ii) $\text{gcd}\left(m,n\right)\notin \left\{1,3\right\}$; (iii) $\text{gcd}\left(m,n\right)=1$ and $4\mid n$ or $6\mid n$; and (iv) $\text{gcd}\left(m,n\right)=3$, and if $n=6$, then $p\mid m$ for a prime $p\le 37$.