I use freezer paper (with a hole punched in the middle of whatever shape I'm using for easy removal later) and a bit of glue (repositionible -I don't think that's a word, but if you only use a tiny bit of Roxanne's or Elmer's or glue stick, that's fine too, even if you've ironed it).
I would think you have to handle the sharp point just like you to in needle turn applique, where you fold over one side completely, trim some excess fabric, stitch the point and then fold the other side.
Let me see if I can you a good picture of that particular technique.
And I'd nick whatever needed to be nicked to cleanly and smoothly fold the fabric over the paper. So, yes. ;-) The outer curve just might not need as many nicks as the inner curve.
eta:
Check out this video - FF to the :50 mark and watch what she does with the fabric - you'd do the same, except with thread or glue (depending on your choice of EPP method).
http://www.youtube.com/watch?v=spjJD78DJWk