In writing these unit tests, I found http://www.printablejewishcalendar.com/ which produces a nice output for each month. And, given that Cheshvan, Kislev and Adar are the only variable months, it was fairly easy to work out the following:
Year   Cheshvan  Kislev  LEAP?   TYPE
5769   29        30      No      Qesidrah
5770   30        30      No      Shalem
5771   30        30      Yes     Shalem Leap
5772   29        30      No      Qesidrah
5773   29        29      No      Haser
5774   30        30      Yes     Shalem Leap
5775   29        30      No      Qesidrah
5776   30        30      Yes     Shalem Leap
5777   29        29      No      Haser
5778   29        30      No      Qesidrah
5779   30        30      Yes     Shalem Leap
5780   30        30      No      Shalem
5781   29        29      No      Haser
5782   29        30      Yes     Qesidrah Leap
5783   30        30      No      Shalem
5784   29        29      Yes     Qesidrah Leap
5785   30        30      No      Shalem
5786   29        30      No      Qesidrah
5787   30        30      Yes     Shalem Leap
5788   30        30      No      Shalem
5789   29        30      No      Qesidrah
5790   29        29      Yes     Haser Leap
5791   30        30      No      Shalem
5792   29        30      No      Qesidrah
5793   29        29      Yes     Haser Leap
5794   30        30      No      Shalem
5795   30        30      Yes     Shalem Leap
Another bit of help is just to have a listing of the Hebrew months. The API declares Nisan as the first month and Adar (or Adar II) as the last month of the year:
  1. Nisan
  2. Iyar
  3. Sivan
  4. Tamuz
  5. Av
  6. Elul
  7. Tishri
  8. Cheshvan
  9. Kislev
  10. Tevet
  11. Shevat
  12. Adar