I love to hand applique. I've made several applique quilts over the years. I've never quilted through the applique. If the piece is too large to leave unquilted, I find some part of the motif and repeat that in hand stitches on the inside of the applique piece. I always quilt around the applique piece as well. It makes a pretty pattern on the back of your work.
When I first began, I tried all different methods because I was intimidated by the needle turn method. Thankfully there was a really good appliquer in my mini group who did that method and she patiently helped me learn. That's the only method I do now. I agree with you Norah regarding the sharp points and inside "Vs" can be challenging. Just take your time at those places, and take tinier stitches closer together and that should help. :)