I think the grip is highly complex and hasn't been done justice by instructors. Usually the recommendation is to just keep the hand relaxed. Maybe it is because the grip is such an individual thing that it is hard to recommend a "one size fits all" instruction. To me, the goal is to deliver the cue straight and without any twisting. I might achieve that differently than you.
I tried something recently that might interest you. I found that I wasn't able to play much on my home table due to "life" but I decided to force myself to hit 1 rack of straight pool break shots twice per day, no matter what. Of course that quickly became once per day... I hit a break shot from the left side then the right and back to the left until I hit all 15 balls successfully. I used different angles and speeds from medium to hard, and forced awkward positions like leaning over the table using a long bridge, and so on. Besides making me much more automatic on the all important break shot, it taught me some things. The primary thing I found is that if I did not maintain a thumb straight down (ie, straight wrist) throughout the shot I would curl the cue which, for me caused left spin on the cb and often a miss. This happened more on stretched out shots and harder hits. Finding that wrist problem was a small magic bullet that has helped, of course, with all shots. I realized that when I am playing really well that wrist is not cocked. (I know some players "pre cock" the wrist inwards because I guess it is easier to shoot that way under pressure but I don't care for that method, at least not right now). So maybe you can pick some exercise shots like I did and take note of what works and what doesn't. Finding the little things that really matter is not usually easy, more like trial and error. I found using the straight pool break shot was a reasonably difficult shot that resulted in a miss when everything was not done correctly, so it gave me opportunities to figure out what I was doing wrong.