If the top player leaves their head up, you can catch their head with an s-grip and sweep down to the side they are sitting on. If they react early, they won't get swept but they will have to turn back into to you, which will put them back in half-guard.
Reaching underneath the arm can be dangerous, it hands the top player a kimura. But instead of leading with my hand, I lead with my elbow and that allows me to get enough of my forearm underneath their armpit to create a frame, which I use to turn into them and create room for a scramble.
Einstein has a great way to set up a darce from the bottom of twister side control. If you ask nicely, he may be willing to share it with you.