The resistor mod really only helps if your throttle has a large dead band at the beginning. You can test this by lifting the wheel and see how far you need to move the throttle before the motor starts. By very slowly advancing the throttle, you should be able to make the motor spin slowly and gradually pick up speed. If you have some kind of sudden jerk when it starts up, you may have a different problem. Since your new motor is the same as the old one, I would have to assume the issue is with the controller.
To try the resistor thing, I would get a 200 ohm, 10-turn pot and insert it in line with the throttle ground wire. Once installed, you adjust the pot until the motor just starts moving, then back off a little.
I've had to do this on a couple of my scooters in the past and it made a big improvement.
The link for your controller needed permission to view. Many of the new ones have some kind of programmability.
One my standup scooter, the throttle was integrated into the display and installing a resistor was not practical. On that one I took a very small chunk of magnet and glued it near the throttle hall sensor to get the same effect. It took some messing around to find the right magnet position, but once installed, it worked very well. The idea is to flatten the throttle curve near the beginning so it is more gradual in the low end. Most hall throttles are very non-linear and start out gradual, then get really steep in the middle. If you have a large dead band at the bottom, the gradual part is bypassed and the motor starts in the steep part.