Guy's equality conjecture for complete graphs in specified genus ranges

Let $K_n$ be the complete graph, let $S_t$ be the orientable surface of genus $t$, and let $\delta_t(K_n)$ and $\mu_t(K_n)$ denote its Euler excess and skewness, respectively. Guy's equality conjecture. If $n=6m$ for $m\geq 1$, then

$$m-1\leq t\leq 2m^2-3m+1$$

implies

$$\delta_t(K_n)=\mu_t(K_n).$$

The claim is presented as a consequence of a construction based on pair-of-pants cobordisms and handles, and gives equality throughout the stated genus interval for this divisibility class.