Thanks to Mark, our visiting purple, for putting some thought into a question of mine... we'd talked about kimuras from side one morning, but I complained that people don't usually make the mistake of waving their arm in front of your face and instead reach high over your back.
His answer is to quickly (avoid being rolled) tuck the headside arm under their neck (from the far side to the near side) and go N/S, which levers shut the angle between your humerus and your ulna. If you put your head on the mat next to their near shoulder/clavicle (not leaving it on their sternum like I always did, grrr) you often can tap them from there-- if not, just gable grip and flex your biceps for the choke.
Nice. Thanks Mark!