Is there any way of installing several versions of the app so that you can choose one just before you start flying, then try another if you start getting problems?
With some apps yes. There are app cloner utilities out there to give each version a different name.
I use 2 different versions - the latest official so things like 360 panorama work and a much older one from before the date DJI broke the android "auto sync HD" download feature they dont seem interested in fixing.
This should be interesting when the mavic Pro two comes out. People that wanna hang on to their original mavic will have to get another tablet or phone to fly both.
Because if you're using an old version of the go app I don't think the mavic two will be in the drop down menu. I'm already using two older versions on my Android phone and iPad. I know it's possible to run two versions on an Android phone but I haven't tried it on a IOS device.