Ryan,
What happens when you apply a hillshade function to the mosaic dataset? You know you can make a reference mosaic dataset from the original right? One would have the hillshade function, and one would be the dem, both from the same source data. If you have Support I would suggest creating an incident so an analyst can connect with you.
Also, in the blog I sent, there is a link to another blog that only uses functions, rather than the image analysis window to create the hillshade and layer tint. The other blog indicates you need a colormap file though, which you would have to create.
Lastly, have a look at the shaded relief function. It's like hillshade but it colored.
Best,
Eric