You don't need to be perfectly on the circle centreline to find the centre. Just position the gear so that you can use an edgefinder/DTI to find centre in 1st axis (X), then move to the centre position in X and repeat the procedure to find centreline in 2nd axis (Y). Double-check the 1st axis. Done.
The most accurate way to ensure the gear is sitting perpendicular to the spindle is to machine a fixture plate 'in situ' that will accept the gear and locate the appropriate face/diameter. Clamp over the part/fixture mating faces (ie don't clamp over 'fresh air') to eliminate clamp-induced distortion.