I would recommend the following to improve transitions:
The end state is the ability to look at the point on impact on the target and have your body subconsciously move the body/arms/hands to align the pistol, ending in a subconscious trigger pull cycle when an acceptable sight picture is attained.
Unfortunately it will take a long time to de-train the conscious effort that most shooters use to manipulate the pistol and pull the trigger.
Regardless of the target set up in the practice session, experiment with the following steps:
1. with a holstered pistol, look at the first point of impact on the first target
2. upon the start signal allow your body to execute the draw - aim - trigger pull sequence without consciously trying to go fast or accurate (this will obviously be very slow at first but gets faster as you practice it). The goal is to use your visual point of impact as the conscious focus and for everything else to happen automatically.
3. add a second and third target with the idea that the transitions also happen subconsciously (no deliberate effort to moving the pistol to the next target)
This is hard to describe without showing you the particulars so let me know if you have questions.