Besides turning off the iPhone completely, can you separate the watch from the iPhone with a setting?
When I am playing pickle ball at a large venue, often times I will find myself on a court that is on the edges of Bluetooth range and the signal sucks but in order for the watch to work independently of the phone so I can use the music stored in the watch or cellular radio stations I have to shut the phone down because even on the outer edges it will continue to look for it and use the phone for support.