Don't try to put your support arm's hand near your head. Keep it on their back shoulder.
There are 3 things affecting the choke:
1. your right shoulder against their left shoulder, pressing on their left carotid artery. You could use your chest against the shoulder, but that doesn't work well when you start doing the baseball slide/Marce finish and the full mount finish.
2. your right wrist/forearm cutting up into their right carotid artery. Too many people shoot the choking arm too deep and end up with a neck crank. Use the rule of thumb, as you should be able to make a thumbs up sign along the back of their neck. This should have your wrist rested nice and solid in the crook of your support elbow.
3. Your left elbow sucking their head in, tucking their chin, keeping their head down almost like pulling someone;s head down in a triangle choke, except your support tricep/elbow is locking the head in.
Keep these 3 principles in mind any time you finish a Darce from top-side control, on your side clocking in, or after stepping over to the full mount to finish the choke.