Another option is to keep the cross grip on the sleeve. This works particularly well if your sweep is only partially successful (just makes your partner sit down momentarily), so they're not extending their far arm into your chest as a sacrificial armbar gift. While you have the sleeve with your right arm, use your partner's forward momentum (remember—they are trying to come up on top to avoid giving up the mount) to drag the arm across. From here, it's once again the familiar cross-grip series, punching their sleeve all the way across their body to your far hip, and then grabbing their armpit.

Of course, if your partner doesn't immediately respond to this threat, you can simply take their back by climbing around. If they try driving into you, you can sweep them to the side, straight to mount or S-mount. Of course, they're likely to try to posture out of the trap, and that's your best opportunity to hit the armbar from guard, using a foot on the hip and then angling out for the finish.