I suggest an optical comparator. From the drawing it looks like you are able to lay the belt flat so the pitch dimension is horizontal and a linear length, not a curved distance (maybe using weights to hold the circular belt in a flat plane). I commented earlier that virtual features can be difficult to measure consistently with handheld tools. The center of the tooth (maybe you call it a thread), which is the start and stop of the dimension, has no physical feature on the part to align the caliper blade against. The centerline of the tooth can be located on a comparator with some arithmetic; if you have an optical measuring device with software the centerpoint of a edge can be identified automatically. If your customer or design team is willing to consider an print change, it is the outside surface of the tooth not the centerline which is the functional feature. If the teeth are symmetrical and uniform in shape, the distance from the corner of the first tooth to the same corner of the second tooth is equal to the distance on centers. Using an optical system you could also measure the distance along the pitch plane, which is truly the functional dimension of a spline or gear-form.
If you still want to use calipers, maybe you can measure the distance from fillet at the root of one tooth to the opposite fillet on the next tooth. That would be pitch distance plus one tooth width, but it would be easier to measure with calipers than a corner which is not a right angle, and therefore more consistent. Subtract the tooth width, measured the same way, if you must have the pitch dimension.