I'm having trouble wrapping my head around the ERD for this database, as well as the correct table structure within FM. Will I need multiple TOs of these main subjects?
In all likelihood, yes. The primary reason is no closed loops are permitted on the Relationships Graph. That means you can't have two join tables between any two given tables, because that would create a loop.
So you would create the join tables as normal, but use different TOs to attach them to the parent tables.