Any tips or drills that can help me achieve that? The front sight moves so quick, by the time my mind processes what I'm seeing the front sight is pointing downward.
It's perfectly natural for the gun to go through a couple of nods when it recoils. And I seriously doubt that anyone can or should track the sights during that rapid sort of kick and resulting wobbling around in our grip. The whole thing takes something less than a 1/5 of a second to damp out. And THEN it's time to notice where the gun is pointed.
But if your sights are pointed down a little when it settles down then you are unconsciously fighting the recoil and might even be seeing a bit of flinch. When the gun finishes up you should still be pointed darn close to the original sighting point instead of lower.
Doing this is the core of the classic double tap or rapid fire string where the shots stay in a tight group. Shooters doing a quick double tap are relying on their hands being a good shock absorber and restoring the gun to the last aim point. But they can only do this if they are not trying to fight or tame the recoil through a reaction to hold the gun in place.
Don't do that. Let the recoil happen. If you fight it you'll never achieve truly good accuracy. Instead use the basics that you are already using and do them really well and altogether. You'll shorten up the duration of the recoil wobble and be ready to do rapid double taps that hit close to each other by using the good high hold with the gun sitting deep in your grip and the turn out of the elbows to convert more of the guns energy into a straight back and forth kick. These are the basics that you are already doing from what a lot of us are seeing.
You perhaps just need to focus on them and do them a little bit better. Noticing that you are pushing away your strong hand's grip on the backstrap is the first step to self analyzing your hold and arm positioning. Keep at it. In the end you are your own best critic to feel what is wrong. There's nothing glaringly wrong with your style. So the improvement is going to come from the little things.
As for reloading and other practices not actually involved with the shooting I'm a big believer in practicing what I will need in matches. And part of that is 100% muzzle and trigger finger discipline at ALL times. We'll do just what we practice when the chips are down. So it pays off later if we practice correctly at all times.
This can have funny results at times though. One day I was airgunning my way through an IPSC stage counting my shots and figuring out my footing and mag changes. Someone walked in front of me and my instant reaction was to raise my pointed finger up so I didn't sweep them. I instantly felt a little silly. But hey, while amusing it showed me that I was using the optimum muzzle safety practices. And that's never a bad thing.