Is it safe to wire an AC-DC adapter directly to a DC motor? (with this setup...)
If the motor 3.25 A locked rotor current and the 6 A power supply output current rating are reliable, that should be ok. A lot of power supplies have over-current protection that is quite sensitive and shut down when a motor is switched on.

I would be concerned about the motor current at full speed. Your 5.9 V test would have only driven the motor at half speed. Even the 1.8 amps that you measured may overheat the motor depending on duty cycle.