I'm assuming that you state most of your work has to occur without a timer due to other shooters. Look into the ShotMaxx2 shot timer - it's worn like a wrist watch and has the option for an accelerometer to be used instead of a microphone for the timer, making other shooters irrelevant, while also having a microphone sensitivity that can pickup airsoft (great for dry fire).
I think a major confusion that you have with shooting fast based off your post is the attempt of using muscle to keep the gun from moving under recoil. Who cares about that - let's care more about getting the point of aim back to where it needs to be as quickly as it can as consistently as possible. You won't get a natural point of aim without either a lot of practice and muscle with precise focus for consistency, or you can apply the skeletal structure which always functions the same to the same forces, and then use muscles to refine as needed. Your call.
As Ron Avery put it - strength helps, but more from a reserve of strength standpoint (so you aren't having to go at 100% all the time). There are also a LOT of champion shooters who are not as strong as other champion shooters, so technique is king.
This video is not to highlight skill - it was one of my worst sessions in the past few weeks, cold, and using a cover garment with this pistol that normally doesn't have a cover garment, and the hoodie didn't exactly stay out of the way. Mental frustrations and cold took hold really quick - but if you're struggling on the A zone at .5 second splits (which you may be slower or faster, as you said you don't use a timer, so let's discount all of that discussion), you'll get far more help attending any pistol class beyond basic NRA to look into the fundamentals of what you're doing than just slinging lead and sticking to the same mindset.
The bill drill was stupid slow - 3.85 seconds. I'm usually in the 2.5 or so second range, which I still consider slow for this gun/distance/etc.