This one's worked for me a couple of times:
Shrimp like a muthafucker and use your arms to get him down towards your hips and off your chest/shoulder. Once he's off your chest you can crossface from the back with your left arm, S-grip or gable lock your hands (I've found the sweep to actually be a little easier with an S-grip. I don't know why though) and sweep him over to your right. It's not a high-percentage sweep and once a guy knows you can hit it it's pretty easy to prevent but it's an available option. You risk giving him your left arm by trying to crossface and if he's not down by your hips and/or has really good base in TSC he can take the arm without much trouble. You're also risking giving him the grapevine while you're shrimping so be mindful of your legs. Don't let him lace those up. Make sure you have taken as much pressure off of your torso as possible before sweeping and move fast before he gets the chance to fishnet your legs or gets his hips back up. It's most successful for me when he's leaning back a bit already in TSC instead of keeping his bodyweight forward and across the chest.