Moving to a more complex squat will magnify any aspects that need work.
If you have deviations from the standard for the back squat address those before moving to a more complex overhead squat.
Always start with the spine.
The spine is the carriage or chasse for the primary engines of the shoulder and hip.
Disorganized at the pelvis hip function is decreased.
Changing the position is the way to improve the function.
Some of the things you are experiencing are downstream issues of the hip.
When you are in a good position your body turns on.
When your body is in a poor position it does not turn on.