Be careful with your transformer selection. I would not expect the limited secondary to secondary isolation of a dual output winding general purpose transformer to be sufficient for the needs of that project.
Option 1: A four winding transformer - four different coils on a closed U core. Signal Transformers "Flathead" series as an example. Others make similar stuff. Standard product with high isolation.
Option 2: DC feed the box and use two commercial high isolation voltage dc-dc convertors.