Obviously, the best advice will come from the known fast guys, like Deuce & Junky on this topic.
However, I can share my experience in my own evolution, & I have decreased my stage times significantly over the last year, & that year over the previous. Here are some things I have learned:
If I try to shoot fast, I jack a round. If I think more about fast than hitting every single target every single time, I'm going to jack a round.
I decide on a cadence, ESPECIALLY for a dump, or 4+ shots on a target that is safe for me, & it isn't as fast as I think I can shoot.
I practice, usually 300-400 rounds/week. I'm fortunate to have a setup in my backyard with a mountain as my berm.
If I have a misfire, I give the mainspring a quarter turn tighter.
If it's a cold day (like 35 degrees or colder), & I'm at a shoot where I don't get a warmup stage to test everything, I'll tighten the mainspring a quarter-turn anyway, cause I know it's more likely to misfire on a cold morning.
Even if it's a dump, focus on every single shot hitting the target. If you do that, & if you practice at least once/week, the speed will take care of itself.
It's a lot like golf, as others have pointed out before. If you try to hit the ball hard, it doesn't work out. If you swing smoothly & correctly, you'll be amazed at how far the ball goes & how well things turn out. That's the only thing I learned at golf, because even though I played regularly & faithfully once a year, I never got any better.