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I'd change the shortcut to point to a script. Then set the script to handle the killing of the old processes> maybe a short wait> check no other chrome processes are running > Start the correct shortcut And update the script icon to match whatever icon the user expects so they don't have to think about the diff

Yeah that might be an idea, avoid the Chrome process start by not actually running Chrome from the shortcut

Yes build it with a loop that kill chrome until no chrome process is available, then start the new one