I might be missing something here, but this might work:

Create a class that derives from PropertyDateControl and override the CreateEditControls or perhaps the SetupEditControl method. In this method, set Visible = false for the EditControl (or somehow disable it) IF the Name property equals "PageStartPublish" (or whatever it is). Then in your global class, use the Application_Start event handler to replace the PropertyDateControl with your derived class using PropertyControlClassFactory.Instance.RegisterClass.

I mean in admin mode, without change the code.