Chris Brennan teaches a great roll thru kimura from the bottom of north south.
^ I'm skeptical. I'm sure it's possible, but in my estimation, if you're thinking about subbing a guy from under north-south, YOU'RE the one who's just about to get tapped, probably with a Kimura or an armbar.
actually you roll thru and finish on top. the kimura grip provides the leverage for the roll.
When I do get a good escape off from north-south, I like the old standard escape of pushing off their hips and then bringing one of my knees in to keep the space I've made. Then I can spin inward and reguard, or possibly use my knee to push off to create a little space and spin back toward guard. Hard to pull off, but there's pulling yourself up onto their back, or the easier version of trying to pull yourself up onto their back, get one hook in, and then just turn in to take half guard instead.
For all of those, one detail that really helped me for the initial space making is locking your elbows out. Because of the normal rule everyone is taught when they start: "don't stick your arms out or you'll be armbared", it doesn't seem "right" at first. Though in opportunities where you are able to make some space by pushing off of their hips(one hand in each hip pocket), it really helps to lock your elbows out to help keep that space while you work to get your legs in to pivot. Since you have control of their hips, you can keep them at bay and feel them coming if they try to attack your arms. Without locking your elbows, you end up trying to keep them up as if I'm half way through a bench press, and I can never hold that for very long.