Double Ditto. If the slower throttle ramp helped but still cutting out, it sounds like the battery is the weak spot. It can't supply the current and the voltage is dropping. You wont' see this with a battery checker because the droop happens when it under load. When you release the throttle the...
Traxxas says there is "no limit"
https://traxxas.com/products/parts/escs/vxl3s
So it "should" work with the motor, but you may not get more speed from it.
Changing the motor and or ESC may not be the answer. The amount of energy to propel you car to what every speed is the same regardless of...
Sorry for the long explanation. Cutting to the hase, I see two things. ESC and Battery. I would start with the battery first, because it will be a limiting factor even with a better ESC.
Starting with the free changes first, check your ESC Low Voltage Cut off (what @Tunedpipe said). It could...