I see nobody's responded to your question so I'll just throw out an idea. I don't have any experience with spraying on a sound deadener. I used a stick-on sound
sound deadening mat on the exterior my doors (under the door panels). But, you might consider using undercoating spray. You can get it at any auto supply or Wal-Mart. Just be sure you have all the glass and mechanial hardware removed or it might be a mess to clean up.