Greekman
I do the same thing when I take new shooters to the range. I start off with the basic safety rules and operation of the firearm. I will often use just a slide or just a frame when doing these kinds of talks so we can see and touch. I do that to confirm that I have an empty gun. I do prefer to do that with a blue gun but it is often left at home.
In my opinion the order of the rules is a whole lot less important than the message. I do like your see the gun touch the gun approach it is an interesting add that I have not seen. I tend to show the interaction of the rules "always treat every gun as if it were loaded so never point it at something you are not willing to Shoot/destroy" type comments.
I will say that your approach does add an element of putting the rules into a process flow, but I am not sure it is a process after you pick up. Never point also applies to your legs and feet as well as those of others. I might argue that before you raise the gun you should assess the fore and back ground. This is especially true of situations where you are not on a square range. Foreground and Background scanning gets harder if you through an optic in or close and eye. I know that goes beyond the IDPA mindset, but so do the 4 rules.
I am not saying that your method of teaching is all wrong and applied as a new student is picking up the gun for the first time is very good. Once that is introduced then the student/friend/family must take it to the now you have to do that all at once and the entire time the firearm is in your hand/control. I do believe that as in introduction it could be a good approach, but it must be reinforced that they are not a 1, 2, 3, then 4 step process but all at the same time.