Two problems with that setup:
The pinion is to big so you will have around 10cm of movement for one revolution of the motor
To much vibration at low speeds
Resulting in jerky movement and the end result.
Lowering the current to the motor will mitigate both problems to a certain extent, at the cost of speed and acceleration.
From experience, you need about 1-2.5cm of movement per motor turn, so use of reduction is necessary.
Move the motor to the side and slap 2 pulleys at 1:3 to 1:5 ratio, that will do nicely.
Do try it as is, later you do improvements.