Should I report my cured mild PTSD in the FAA medical certification application?
Unfortunately, you have to report it.  It even says so right on the medical application (emphasis added by me):


  18) Medical History - HAVE YOU EVER IN YOUR LIFE BEEN DIAGNOSED WITH, HAD, OR DO YOU PRESENTLY HAVE ANY OF THE FOLLOWING? Answer
  "yes" or "no" for every condition listed below (All "yes" answers
  require a comment. Click Add Comments to add or edit a comment).
  
  ...
  
  Mental disorders of any sort: depression, anxiety, etc.
  
  ...


Based on your own admission, you had it at one point and are now cured.  This means that you have "at some point in your life" been diagnosed with it.  

Unfortunately, the FAA takes a very hard line on this kind of thing and it does not surprise me in the least that they are now requiring a battery of expensive tests in order to prove that you are fit to fly.  I don't like it either, but it does keep the people out who "say" that they are cured when they aren't, either because they don't realize it or because they just want to fly anyway.

If it is denied, then you can appeal it, but I would suggest getting good professional help.  As voretaq7 mentioned, AOPA has a very good medical service that helps their members for free.  Membership is pretty inexpensive, and more than worth it just for this service, plus they have many many other benefits as well.

A couple of other questions on the site that may help you:


FAA Class 3 Medical re-examination
Can a private pilot receive recurring training while waiting for a special-issuance medical approval?