Getting to know your swing and your pattern is the first step. I agree with your overall assessment. Let me try to add a couple connections for you.
At the top of the swing, your arms have worked more around your body (instead of finishing the backswing with your body). This makes your arm height a little flat. This coupled with your downswing early extension produces an overly in to out path (producing your big draw pattern).
The arms getting behind your body loads the shoulders. The little steepening move at the top indicates that you're pulling more with your arms to create power and then your upper body drifts forward through the release (not much bracing).
Tackling it in pieces, I would probably work on either the backswing width or the transition sequence. I'd monitor how that changed the look of the forward lunge. I'm not sure which I would go at first, so in a lesson, I would probably try both to see which had the bigger change.
I'd experiment with the trail arm width, or the transition pump. Keep me posted!