Your question relative to your glove arm is a good one. Most pitchers in their early stages do not give justice to this body's function while progressing forward.
My suggestion to you would be to notice the feel of your body's balancing sensors as you progress down the slope of the mound. Like any forward motion involving the entire body, your arms provide a "non elected response" to your feeling the movement. Hence, pay particular attention to that glove arm (in slow time). Watch how it will stretch out to a point - then stop. At that point of stop, more often than not your stride foot is directly under that glove. And as such -- as the glove arm swings out .. so does the body's tendency to follow suit with the everything else .. hips.. torso, etc. In fact, if your performing off a very poor pitching surface and you have a video camera, watch in slow motion how this gove arm actually leads just about everything else.
With constant practice, you can keep your hand(glove) of the glove arm inside the stride leg's thigh as the rest of your posture starts and complete its routine.
First do it the old way .. the way your use to doing it and video it.
Second, deliberately concentrate on keeping the glove hand back a bit as you start you progression from the leg lift .. then as your stride leg stretches out .. follow behind with that glove arm .. but keep the glove hand on the inside of the strid leg's thigh. Once the glove arm is where your accustomed to stop'g it -- move your chest TOWARDS the glove.
I've used this methods over the years and it works perfectly. Also, it helps if you explain this to someone else so they can stand next to you and observe and give you some feed back. You should also notice a real upbeat in the pop in the glove of who's catching for you.
Please post back and let me know how you did.