Do you have any advice on how to improve my overhead squat (other than actually overhead squatting)?
better thoracic spine and shoulder mobility and stability.
This.
Shoulder dislocations w/ stick for shoulder mobility.
Thoracic extensions on roller for thoracic.
If your hip and ankle mobility is lacking these will also ruin it for you...but I'm sure you know how to fix these.
For stability
-snatch grip overhead press
-snatch grip behind head pull apart with rubber band, really squeezing traps hard, to make harder you can lie on floor and do this behind head too
-spots presses, and klokov 'deep squat barbell front raise to overhead'
Are pretty much what I've done and has helped me.