I risk straying out of my lane here, but I worked on draws and controlled pairs to a 3X5 and the credit card and a USPSA target yesterday. Like you, I am frustrated with my first two shots. Normally my first shot speed is around 1.8 to 2.0 with a .5 to .8 follow up shot. So there is a lot of juice I should be able to squeeze from that.
So yesterday I decided to take the brakes off and shoot it like I normally would in dry fire. I decided to focus on trigger press, working to jam the trigger straight back. I was really surprised with how loose a sight picture I could have and still get acceptable hits. It was a lightbulb moment. After half a dozen mags I was able to get consistently down to a 1.4 first shot with a .3 follow up. It went so well I switched to the USPSA credit card and really didn't have to take my foot of the gas to get my hits, I only dropped 3 shots in 30 rounds. I think it was TG that said that sometimes you have to go faster to get faster. I believe that idea applies here.
I think these types of shooting problems, and true mastery of them, require a lot of rounds down range to solve. Dry practice will only get you so far. My main limiting factor in improving my shooting is live fire so it takes me longer to figure out these issues.