I hope I didn't misunderstand what you are trying to do. Here is my solution. Install the T and valve at the far end of the hot water line. Return the water to a T just before the intake to the water pump (not to the fresh water tank). This will recirculate the cool water and you will not be adding any warm/hot water to your fresh water tank if you get distracted for a short time. This will allow you to still use the cool water in the water line and not fill your grey tank (and conserve your fresh water).
Hope this helps. Good luck with your project.
