Paps do not always pick these things up, sometimes they go undetected. Thats why regular paps are sensible.
Seeing as your at the severe/moderate stage, the Dr will most probably suggest some treatment to stop the cell changes from getting worse
I have no idea how they missed it on the pap, but it doeshappen I have heard. I have CIN III also and am having a LEEP next month. The margins not being clear means prob they will do another procedure. IDK not there yet myself.