Singer graceful-graph conjecture for finite-field graph decompositions

Let $[m]_q=(q^m-1)/(q-1)$ denote the $q$-analog of $m$. A graph is Singer-graceful when it satisfies the graceful-labeling condition associated with the Singer difference set. For integers $v$ and $i$ with $1\leq i\leq [v-2]_q$, let $\Gamma$ be a regular graph of order $[v-1]_q$ and degree $qi$. Singer graceful-graph conjecture. The graph $\Gamma$ is Singer-graceful, and consequently there exists a cyclic $2$-$(v,\Gamma,i)$ design over $\mathbb{F}_q$. This is presented as a specialization of the preceding difference-set conjecture; it would produce an infinite family of non-trivial graph decompositions over finite fields, and the source gives no resolution.