Never have equipment on when changing plugs, it courts disaster.
Also changing HDMI plugs is a very bad idea. HDMI plugs and sockets are fragile and you will damage plug, socket or both fairly quickly.
You might want to consider HDMI over Ethernet cable rather than active cables which have another set of problems.
Best of all is not to have equipment far apart. Much better to have discrete systems in the spaces you want to use. That works best and is the high road.