OMG, I have exactly the same problem, the hair at the nape of my neck is poker straight too.
It's about a one inch section, annoys the hell out of me because the rest of my hair springs up 3 inches and the straight bit is visible.

My stylist also recommended perming it but I haven't gone for it yet.

As a quick solution try damping it and braiding it before bed.
3a Redhead
Umberto Giannini & Curls Rock Amp
Fotki pw: curls