Without seeing how complex the information is that you have collected it can be hard to give a definitive answer to your question. But from what you say a VSM could be one way to show where information is being held up if you show the workload that is at each stage in the process; maybe with a work in progress measure showing the number of documents with an average time for processing each.
Be careful when measuring processing time, maybe it only takes a few seconds to sign a piece of paper but they will often sit there for days before being reviewed. I would be inclined to take an average number of documents processed in a specific day to calculate a processing time.
I once did a similar process improvement on the flow of paperwork through a company; this was done as a “brown paper” exercise which took up a whole wall of a large meeting room to map out the flow. Despite showing major hold ups people were still resistant to change – that was until we turned the company CEO into a “document” and walked him step by step through the process, desk to desk, explaining how long he would sit on each desk etc. After the initial explosion and fall out things were soon improved. People were given responsibilities to approve work rather than sending multiple documents through many different departments and other issues.
Best of luck with what you are doing.
Ries and others created an annual technology conference called Startup Lessons Learned which has subsequently changed its name to the Lean Startup Conference.  Lean startup meetups in cities around the world have garnered 20,000 regular participants.  The first lean startup meetup named Lean Startup Circle was created by Rich Collins on June 26, 2009  hosting speaking events, workshops, and roundtable discussions. As of 2012, there are lean startup meetups in over 100 cities and 17 countries as well as an online discussion forum with over 5500 members.  Third-party organizers have led lean startup meetups in San Francisco , Chicago , Boston , Austin , Beijing , Dublin , and Rio de Janeiro , among others—many of which are personally attended by Ries—with the Chicago and New York City Lean Startup Meetups attracting over 4,000 members each.  The Lean Startup Machine created a new spin on the lean startup meetups by having attendees start a new company in three days.  As of 2012, the Lean Startup Machine claimed to have created over 600 new startups this way.