It's been quite a while since I actually practiced with or studied handgun. Quite a while. When I was well trained I shot as well as anybody else who is well trained. When I was most well trained I consistently hit baseballs at 35 yards.
So, I'm back at it. And I am hoping somebody has a trick to speed this up.

I have a target at about 15 yards. I can get a good site picture and hold it on the target well enough to make a hit consistently. When I do my part I'm getting a group about the size of a softball, which is acceptable for now.
However. When I get the correct picture I attempt to slowly start to tighten up on the trigger. This causes the gun to move a little. That get's me freaked out that I'm going to yank the gun off target. Which tends to encourage me to try to yank the trigger at just the right moment when it is on target. Which causes me to yank the gun all over the place.
Either I shoot as well as I want. Or I totally blow the shot by at least a foot. The more I blow the shot, the more likely I am to screw up the next shot even worse.
The fact that I am trying to make each shot perfect is definitely making this worse.
I guess ball and dummy drills will help.
When I was competing silhouette I spent a lot of time dry firing on a series of circles. I would start practicing at a very big circle and make all descent shots. Then a smaller circle, just working the trigger and making descent shots. Then a smaller circle with the goal always to be to make good enough shots without trying to make each shot perfect. This drill and the ball and dummy drill are the only 2 training methods I know of. It takes time and work.
If I could practice more efficiently and cut down the training time getting back to where I want to be that would be much appreciated.
Any thoughts?

Don't pull the trigger so slowly and squeeze the shit out of the pistol. When you decide to shoot something, just shoot it. Thinking about it too much gets you lost in your head and not focused on performing the fundamental task at hand, delivering bullets to something that needs to be destroyed.

Ah. Ok, thanks. I'll have a look at that.

And, yeah. I'm fine at the moment with softball groups at 15 yards at the moment. And that's what I get when I press the trigger properly. But when I start to get freaked out because it feels to me like the trigger should be moving but it is not moving, that's when I start goosing the trigger in an attempt to get it move at just the right moment. And then, I no longer get soft ball groups. The groups get, um, worse. Currently I'm like 50/50 doing what I should I do vs just blowing it.

I'm attempting to develop the correct procedure to practice before I start repeating it in practice. Practicing bad habits is a bad plan.

Accept the wobble, press the trigger straight back, and don't try to break the shot the microsecond the sights are "perfect".

Experimenting with target focused shooting will help you.

In addition to the above comments, MantisX may also be helpful.

You need a better grip. That will keep your sights aligned when you pull the trigger.

What is the end goal?
Bullseye, IDPA, USPSA, self defense?

Self defense, and farm defense. In the past a couple of times I made head shots on foxes at about 30 yards. I shot bowling pins at 30 yards all the time. But I was practicing exclusively 1 good shot. Now I'm drawing from concealment and taking the shot, like self defense. I'm not focusing on my breathing, I'm not readjusting my feet, I'm not readjusting my grip or my trigger finger or anything. I go through the drawstroke sequence and take the shot.
I need to get back to closer to where I was. I'm not, not at all.

I found a small, relatively informal .22 bullseye group near me that helped tremendously with this. It really teaches to focus continuously on the sight while gradually squeezing...almost forget about the squeeze of the trigger as you're doing it since more focus is on the sights. The continuous focus on keeping the sights on the target is the main focus, and it just about can't help being a good hit.

Then just transfer that at an accelerated pace to a larger caliber :)

A few videos to help you!

The main thing is that you learn to press the trigger relatively aggressively without disturbing the gun.  You can make very accurate hits out to very far if you accomplish that.

This is how I typically describe trigger control to others - Trigger Control Video

This is a video that has a bunch of the drill I use to accomplish what I describe from a year or so ago - How to Dryfire

This video will show you how much the firing hand is NEEDED - Firing hand

Enjoy!  Feel free to reach out with questions (I'm not on here a ton but you can send an email to [email protected] :) )