The shine comes from a mix between the intensity of your normal map and how bright your spec map is. I know you probably already know this, but, try baking your normal again or reducing the overall brightness of your spec map. For something that has little to no specularity, your spec map should be nearly completely black.
One other thing to try could be to remove the spec and normal maps completely from the folder and let Reloaded fill in the blanks?
Hope you get it sorted.
Cheers
Jay.
