Good job on the pipeline, it appears to work well!
My suggestion would be to either use MeasureObjectIntensity on the Fibril objects and then examine the value of the edge measurements (IntegratedIntensityEdge, MeanIntensityEdge, StdIntensityEdge, MaxIntensityEdge, MinIntensityEdge) for each fibril. However, my suspicion is that the fibril borders may not extend far enough to the boundary to get a good reading; they're close but perhaps a few pixels short due to thresholding.
So in this case, you might be well served by using IdentifySecondaryObjects on the original image and use the fibrils as input. That way, your new objects will touch and therefore fully cover the bright edge pixels. Then use MeasureObjectIntensity to make your measurements. You also may be able to play further tricks with ExpandOrShrinkObjects to fine-tune how much of the edge each fibril covers.