Donna,
Your procedure and rationale are clearly well thought out and very sound. I expect you have a high level of student success with this approach, as well as high performing graduates. Your statement of "Sticking to your policies is a must" indicates a high level of integrity being modeled for the students, which is an important component in creating an outstanding learning environment.
While I may agree with your 'no exceptions' approach for most classes and situations, there may be circumstances where teachers are required to build flexibility into their deadlines because of institutional policy. Nevertheless, even when flexibility is required as part of the policy, the firm establishment of clear expectations is an essential cornerstone for any effective educational setting.