I think the orthotics and all that rigidity could definitely be contributing to your shin splints. With that much rigidity, your lower legs have to really work hard, causing you to engage your calf muscles. That, and tension in the legs, can cause shin splints.
Try doing a few short runs without the orthotics and see if that helps. Remember the rule of gradual progress - your body is still used to the orthotics so ease out of them gradually. Good luck and keep us posted.
Certified Chi Running and Chi Walking Instructor