On completing three cyclic transversals to a latin square

Let $P$ be a partial latin square of prime order $p>7$ consisting of three cyclically generated transversals. Specifically, let $P$ be a partial latin square of the form: $$P=\{(i,c+i,s+i),(i,c^{\mathrm{\prime }}+i,s^{\mathrm{\prime }}+i),(i,c^{\mathrm{\prime }\mathrm{\prime }}+i,s^{\mathrm{\prime }\mathrm{\prime }}+i)\mid 0\le i<p\}$$ for some distinct $c,c^{\mathrm{\prime }},c^{\mathrm{\prime }\mathrm{\prime }}$ and some distinct $s,s^{\mathrm{\prime }},s^{\mathrm{\prime }\mathrm{\prime }}$. In this paper we show that any such $P$ completes to a latin square which is diagonally cyclic.