Where can I get the FAA data that defines airspace, including MOAs etc.?
Take a look at the National Flight Data Center.  The data appears to be contained in NASR. I mentioned in my comment that there may be no official source for spatial data, but I think this may include what you are looking for.
These are derived products. The cannonical definitions are the legal descriptions found in FAA Orders with the prefix 7400. At the time of this writing, JO 7400.11 (current version E) covered airspace classes A,B,C,D and E as well as reporting points. The JO 7400.10 (current version C) covered special use airspaces. Both publications can be found at the FAA's Website.