Is there any guidance/documentation available on the best approach to take when upgrading an distributed installation of FME server based on the Azure marketplace images?

There's the general FME Server documentation about upgrading that you can use as a starting point: https://docs.safe.com/fme/html/FME_Server_Documentation/AdminGuide/Upgrading.htm

On top of that we always recommend to document your installation process so you can use that as a guide for the next one.