Any-angle path planning is an extension of traditional path-planning algorithms that aims to generate smoother and shorter paths in graphs by allowing any-angle moves between vertices, rather than being restricted by edges. Many any-angle path-planning algorithms have been proposed, such as Theta*, Block A* and Anya, but most of them are designed only for static environments, which is not applicable when dynamic obstacles are present. Time-Optimal Any-Angle Safe-Interval Path Planning (TO-AA-SIPP) was developed to fill this gap, which can find an optimal collision-free any-angle path that minimizes the traversal time. However, as indicated by its authors, TO-AA-SIPP may not be efficient enough to be used in multi-agent pathfinding (MAPF). Therefore, this paper presents a new algorithm Zeta*-SIPP to improve TO-AA-SIPP by means of 1) reducing useless search nodes that have no contribution to finding optimal solutions, and 2) introducing Field of View (FoV) instead of Line of Sight (LoS) to speed up visibility checks with static obstacles. Benchmark experiments showed that Zeta*-SIPP reduced the computation time of TO-AA-SIPP by around 70%-90% on average.