Looking for help with both the north-south position and the kimura from north-south, I found this interesting attack from Marcus Soares over at GrappleArts. It is a variation on the kimura from north-south, with a Frankenstein-type choke/neck crank option.
The first part is essential, and a good control position form which to launch attacks. When in north-south, you want an over/under. Overhook one arm (with the hand on that arm perhaps controling the hips) and underhook the other arm (with the hand probably gripping the sleeve at the elbow to control the upper body). Put your weight more on the side of the underhook.
The guy will probably be worrying about the underhooked arm, the possibility of getting armlocked or kimura'd. The danger, though, is the attack on the other arm, the overhooked arm.
Soares instruction is clear: "Start circling toward the overhooked side and trap his arm by encircling it with your own and gripping your own lapel."
The grip is sort of like a guillotine on the upper arm or shoulder over the overhooked arm. The motion to get there mimics the sort of "tucking the arm inside" that you want to do if you are in somebody's guard and they've got an armwrap on you. Rodrigo's showed me this arm tuck a few times.
Now for the body movement. Switch your base into sort of a Watch Dog position. You want to open your hips up to the underhooked arm side. Slide your near leg under the guy's head like a pillow.
Reach over with the underhook side arm and grab the guy's far collar and bring it across his neck toward you. This also helps keep the guy's head down for the next move.
Flip your other leg over the guy's head and triangle your legs. Try to get under the chin so that it is more of a choke than a crank.
Again, Soares: "Now you lie back and pull on his arm, putting severe strain on his shoulder."
I think you can also work the Frankenstein choke at the same time by pulling on the collar and straightening your legs. Slow, steady pressure should get the tap.
