Strongly regular locally $GQ(4,t)$-graphs

Amply regular with parameters $(v,k,\lambda,\mu)$ we call an undirected graph with $v$ vertices in which the degrees of all vertices are equal to $k$, every edge belongs to $\lambda$ triangles, and the intersection of the neighborhoods of every pair of vertices at distance 2 contains exactly $\mu$ vertices. An amply regular diameter 2 graph is called strongly regular. We prove the nonexistence of amply regular locally $GQ(4,t)$-graphs with $(t,\mu)=(4,10)$ and $(8,30)$. This reduces the classification problem for strongly regular locally $GQ(4,t)$-graphs to studying locally $GQ(4,6)$-graphs with parameters $(726,125,28,20)$.