Here is something you can look at, that is if my memory of what the Haas tech did to fix my HL1 about ten years ago is correct.
At the center of the turret is a ring of bolts that hold it onto its shaft that has the worm gear inside the housing that the servo drives. As I recall the holes for these bolts have considerable clearance and on one of the bolts there is a dowel bushing to align things. I seem to recall the bushing in brass and the tech said something about it being a sort of shear pin that would yield if the turret got a healthy whack while it was locked.
You should be able to loosen these bolts so they are just finger tight and then slightly rotate the turret to realign it. You may have to both rotate the turret and move the X axis slightly to get one of the tool holder holes on center checking with a DTI in the chuck; then cinch up the bolts. Needless to say this is all done with the turret in the locked position.
If the turret then indexes okay and you do not get any alarms about a servo overload, (I think on these lathes the turret servo is called the A axis) then you could be good to go.