NO! The key to the Twister IMO, is to have the control of your opponents hips from a position where he cant spin (Truck) and create a scramble. This is why its crutiel to master the final 3 steps of the Twister. If you release hip control, you better have that arm control before you move on to the battle of head control, or your opponent will simply spin/create scramble/flip the Twister. Even though we have good hip control from Stoner control, the Leg positioning is way off. Even if you switch to the Grapevine, your hips must be facing the same direction to that of your opponents. If you attempt this when your hips are facing opposite directions, you will never get under the armpit in search of 'S' grip head control glory! If you skip going under their arm and just grab the head, he will spin. REMEMBER- Hip control (via controlling the extension of the hips, the legs with Lockdown and correct arm control on their opposite leg-prevents them spinning), when you release your arm control of their leg, YOU MUST HAVE CONTROL OF OPPONENTS ARM or your opponent will spin!
All options from Stoner control are based on you opponents reaction, he will turn- he hasn't many other options. And when they do, we use real Jiu Jitsu, and follow the path of least resistance- which is usually the sweep to Side control. NEVER give up control is search for a sub! GET position, KEEP position, USE the position- Jean Jacques 101.
Hope this helps