For those of you that are interested, I found a solution. Take the original DEM you are working with before converting to a Hillshade and before creating symbology. Run Spatial Analyst> Neighborhood>Focal Statistics use your original DEM as the input file and select a 9 by 9 rectangle. From there use the focal statistics layer to create the hillshade and to create a color map for you hillshade. I have no idea why or how this worked, but I do know it worked. I would appreciate an explanation on the nuts and bolts of why this worked if anyone has one, but for now I'm satisfied.