Hi, Korbinian,
Payara doesn't allow providing an offset to shift all ports. This can be provided only when domainis created. The only thing similar to it is to set all ports to reference environment variables and specify them all before you start Payara Server. Later you could specify different values for them. I understand that it's very cumbersome.
Alternatively, you can create a new domain with a specified offset for ports and then compare it to the default domain. It should be easy to find out all ports that need to be changed. Then it is pretty easy to edit domain.xml manually and update all ports as needed (there are around 8 ports to change). If you want to do that quickly to limit the down time, you can script this as asadmin commands, run the commands when you want to switch and then restart your server.
You may also raise an issue on github to request a similar offset functionality that exists in WildFly.
All the best,
Ondro