It sounds like one or more of the new batteries may be faulty. If you can get to the battery terminals with the batteries installed in the scooter then we would test the Voltage of the individual batteries after the charge is at zero and with the power on and throttle fully engaged. Then you will be able to see which battery or batteries are dropping Voltage under load. If you cannot get to the battery terminals when the batteries are installed then they can be removed from the scooter and then tested. If they all test with a normal Voltage in the 13 Volt range then they will need to be load tested by connecting a load to them and seeing if the Voltage drops.
Yes, individually testing the Voltage of the batteries when they are discharged may help to pinpoint which battery or batteries is causing the problem.