I'm no Master class shooter (yet ) but I'll share somethings that have helped me.
When I practice dry-fire transitions I look at the target, move the gun to where I'm looking, change my focus to the front sight, then look at the next target and repeat.
I find there are 2 main things that slow me down:
1. I can move the gun faster than I can move my eyes/change focus from target->front sight
2. I waste time/movement moving the gun to where I'm looking, by over or under swinging when I try to go fast, or on irregularly spaced targets.
So there is a visual/eyespeed issue, and a hand-eye coordination issue.
To try to overcome this I go in my bathroom where we have a wallpaper with lots of tiny irregular dots. I'll pick a color and just transition from dot to dot in a random pattern for a few minutes. This forces me to be very precise and prevents me from getting into a rut with target spacing.
Another thing I will do is get a good sight picture with no target, and smoothly move my gun back and forth in increasing arcs, maintaining my sight picture and being extra aware of how my body adjusts to keep the sight picture. I've found this helps on wide splits like steel challenge, as I can look way over and bring my gun to bear with sights lined up.