A propulsion system for an aircraft includes a first open propulsor rotor, a second open propulsor rotor, a turbine engine, a first drivetrain and a second drivetrain. The first drivetrain operatively couples the turbine engine to the first open propulsor rotor. The turbine engine is configured to drive rotation of the first open propulsor rotor through the first drivetrain during a first mode and a second mode. The second drivetrain is configured to operatively couple the turbine engine to the second open propulsor rotor during the first mode and to operatively decouple the turbine engine from the second open propulsor rotor during the second mode. The second drivetrain is configured as or otherwise includes a tower shaft. The turbine engine is configured to drive rotation of the second open propulsor rotor through the tower shaft during the first mode.