First, to clear something up. A corked spin is similar to a D-spin, only a d-spin you go inverted, a corked spin you don't.
I used to have the same problem. Here's how I corrected it. Throw it more like a spin than a flip. Instead of throwing down behind you (the 180-misty approach), throw like you're going to do a fast, tucked up 7. However, as you set your spin, drop your lead should just a bit. Think of as you set your spin, looking at the ground about 100 feet behind you to get you started right. (don't focus on it, that's just the axis that you want to set your spin on.) From there, it's all about staying tight, keeping your head in spin, and waiting till you com back on axis. I find it easiest to do with a safety grab to keep you in the right position.
Your first one will feel really odd and you'll probably want to open up early. Don't. Stay tight and the rotation will bring you back on axis. Just takes some practice. Good luck.