Same here. Slapping rough stock in a four jaw isn't about the exterior so much as solid stock below. I don't follow the 3 o'clock method in precisely same manner, but make slight contact to find the 'high side' and give the face a dab of felt pen. Rotate 180*, estimate [or re-position the DI for contact] distance off center. Halving that shows how far to move the part.
Another trick is with chalk. Rotate the item, marking close to apparent center or layout center. The error will be apparent as a starting point. Great for castings or irregular forms unsuitable for DI.
Note to self. Replace a long lost pump or centering wand... thinking about a ball and conical seat, machined in a spring and plunger [maybe half universal joint device]. Most lathes around me are 16" and larger swing, so figuring the wand should be equal length minimum of .200 dia. something drill rod?