UPDATE:
OK I got it worked out, but wanted to post an answer just in case someone else has this same issue down the line.
In order to be able to export out of blender into UE using FBX 7.4 with Shape key animations rigged with Bone Drivers, you have to make sure you un-tick Apply Modifiers. Since you can not apply any modifiers to a mesh that has shape keys attached to it. So when you export and have it set to apply, all of the shape keys get erased when exported. Thus no animations or shape keys area transferred over.
Hope this helps someone else.