I agree with several previous posts that the problem is the small pulley. The problem is that you do not have enough "teeth in mesh". Slowing down and/or ramping will definitely help, but it is band-aiding the problem.
From your video, it looks like the belt is 120T which with 18 -> 36 pulleys puts your center to center at 9.1371inches (using
http://www.wcproducts.net/how-to-belts/) and teeth in mesh of 8.6. This is very low and given the small 18 pulley the best you can realistically do with an idler would be maybe 9.5.
We had nearly an identical belt problem on our intake and switched a 36T to 60T with 140T belt which has a similar center to center of 9.0247inches (slightly tight on the 9.14inch hardware) and 17.2 teeth in mesh. The available torque goes up over 3x. If you are willing remount motors, there are other configurations that are smaller but still get more teeth in mesh. (24T->42T pulley 120T belt, 8.55 center, 11.5mesh)
Good luck and let us know what works for you.
PS: looks like you are already using 15mm belts and pulleys so I did not initially suggest wider belts. The 15mm pulleys can handle two 9mm belts which gives you 20% more width basically for free.