I didn’t work on getting that geometry to converge. I wanted to hear back from you on whether the web that you want to transport can be assumed to have no bending stiffness. This could be a simplifying assumption for very thin web thickness.  Thick belts as as found in machinery are circular when manufactured and a racetrack as the undeformed shape would be silly. What is the web thickness you want to simulate and what is the Young’s Modulus and Poisson’s Ratio of the web material?

To take a circular belt and stretch it into a racetrack shape, take two pulleys tangent to the circle and move one to the stretched position in step 1 of a multi-step solution.  Step 2 can rotate the fixed pulley.