I see four possibilities. one the faceplate is buckled/distorted. Two the spindle register is not square to the axis. Three, the faceplate register face is not parallel to the face. Four, axial play in the spindle combined with cyclic spindle movement.
None of them are common problems. Normally one would skim the faceplate on its own lathe but that's not easy on a wood lathe, (although you could lash up a temporary cross slide).
If the spindle register is true, (check again), then check it again!
When you clock the flywheel face run-out is it always the same position?
If you can get a micrometer through the central hole and measure the thickness between register and face and you have no errors than the faceplate it self must be buckled. If you are lucky and the two faces are not parallel (but the main face is true and flat) you could just carefully true up the register face by very careful filing. Using blue combined with frequent clocking you will have it dead true in minutes.
Oh, Bearings are tougher than you think!
Ian P