Limiting increment conjecture for expected propagation times of n-Suns

For the $n\operatorname{-Sun}$ graph, let $\operatorname{ept}(n\operatorname{-Sun})$ denote its expected propagation time. Limiting increment conjecture.

$$\lim_{n\rightarrow\infty} \left(\operatorname{ept}(n\operatorname{-Sun})-\operatorname{ept}((n-1)\operatorname{-Sun})\right)=\frac{11}{16}=0.6875.$$

The conjecture is motivated by the tabulated numerical values of successive expected-propagation-time differences, which approach $0.6875$. Its status is not established in the supplied material.