1. Belly roll: from the body lock, bridge hard into the guy to get your hips under his, then twist back and roll him the other way into side control.
2. Shoulder lock: from the body lock, put your inside elbow on the mat as you turn to your side very, very close and come up to your knees, then reach over with your outside arm and put that hand on the ground in front of his face. Turning your body, pull your inside hand and arm free and put it on the mat. With both palms on the mat, slowly bring your head up … if he doesn’t tap from the shoulder pressure, then just pull your head out and take the back.
3. Axe kick: from the body lock, reach up with your outside arm and push the guy’s head back toward your outside leg, then lift your leg up and over in front of his face. Pull your leg down backwards and roll the guy over.
What all three scarf hold escapes have in common is the necessity of getting your outside underhook. If he’s got the underhook on the far side, then all of the above escapes can be blocked. So the underhook on the far side (the outside) is job one when caught in the scarf hold.
Based on my very, very limited knowledge of Greco, it seems like the best way to pummel for that underhook is to grab the waist, belt or pants on the inside and tilt the guy into you, preferably higher up on your body. That should help open up space between his arm on the far side and his body. He may even need to extend that far for balance if you can pull him hard enough into you. Keep pulling him into you and looking for opportunities to slip that underhook in.
Another approach that is more jiu jitsu might be to just work to escape your hips to the outside, away from him. You aren’t trying to escape that way, just to get some space so that you can shoot that underhook in.