Circulant construction conjecture for doubly saturated $R(3,t)$-good graphs

For odd $t \ge 17$, let $G_t$ be the circulant graph on $5t-10$ vertices whose distance set is

$$[t-4,t-3] \cup [t+1,(3t-9)/2] \cup \{(3t-5)/2\} \cup \{2t-4\}.$$

A graph is doubly saturated $R(3,t)$-good if it is $R(3,t)$-good and satisfies the paper's double-saturation condition. Circulant construction conjecture. The graph $G_t$ is doubly saturated $R(3,t)$-good for every odd $t \ge 17$. This conjecture is based on computer-assisted experimentation and proposes an explicit infinite family; its status is open.