I can only guess what's possible because I haven't seen inside one.
The battery will be a problem because it's built into the frame, which doesn't leave any room for more cells. The next thing we'd need to know would be the motor winding speed, whether it's that that limits top speed or the controller/panel software. If it cuts off suddenly, it's more likely to be the software, but I'd be surprised if it did more than 40kph even if you could hack the limit. To test the motor speed, you'd need a spare 36v controller and throttle to do a no-load speed test. Any one will do as long as you only test with the wheel off the ground. Use a bicycle computer to check the wheel speed. You only have to put the magnet on the spoke. You can hold the sensor in the right position yo get a speed reading. Once you have the motor speed, you'll know whether you've got a chance of achieving anything with a new controller. You could in the meantime get a photo of the controller so that we know what it is.