slide non-choking hand behind head, not on top.
Do not fold the hand that goes behind the head over the choking hand. Put it there independently and then slide the choking hand to the arm.
Elbows squeeze together. Squeezing with back, not biceps. Hips extend. Head tight pushing opponent's head forward. Hand behind head makes fist also pushing head forward. Opponent's chin in line with choking arm's elbow.
Just some quick things jotted down.