A drone swarm is a robotic architecture having multiple drones cooperate to accomplish a mission. Nowadays, heterogeneous drone swarms, in which a small number of gateway drones (GWs) act as protocol translators to enable the mixing of multiple swarms that use independent wireless protocols, have attracted much attention from many researchers. Our previous work proposed Path Optimizer — a method to minimize the number of end-to-end path-hops in a remote video monitoring system using heterogeneous drone swarms by autonomously relocating GWs to create a shortcut in the network for each communication request. However, Path Optimizer has limitations in improving communication quality when more video sessions than the number of GWs are requested simultaneously. Path Coordinator, which we propose in this paper, achieves a uniform reduction in end-to-end hops and maximizes the allowable hop satisfaction rate regardless of the number of sessions by introducing the cooperative and synchronous relocation of all GWs. Path Coordinator consists of two phases: first, physical optimization is performed by geographically relocating all GWs (relocation phase), and then logical optimization is achieved by modifying the relaying GWs of each video flow (rerouting phase). Computer simulations reveal that Path Coordinator adapts to various environments and performs as well as we expected. Furthermore, its performance is comparable to the upper limits possible with brute-force search.