The old saying applies: You can take the horse to the water, but you can't make it drink.
As others have pointed out, what should really matter to this senior director is business value. You could try to provide a quick estimate of how much time you are going to spend drawing up his flowcharts and module diagrams and writing a "complete" SDS (ridiculous concept, but give him what he wants). If I know anything about these things (and when I started writing software, that was the way it was done) then your estimate will easily be several man weeks, if not more for a sizable project. Express that figure in money.
Then show him how much functionality you could deliver in the same time. Talk to a few people in the business on how much time it would save them to have a basic web app doing those things you could deliver in that same time. Then multiply this saving by however often they use this function in, say, 3 years. Express that in money.
There are probably other business benefits that can be expressed in money. My favourite is always "goofball" prevention. If your software can help to minimize disasters or avoid them altogether, then find a recent disaster and express it in money terms. Then say to your boss: If we had this right now, we would have saved this money.
And if the money trick doesn't work, then maybe should walk up to him and tell him to stop micro-managing his team. Although, in my experience, that is more likely to get you fired than anything else.