A couple of cautionaries. Spur centers were designed to drive in end grain. They are prone to cam-out in face grain, so consider your face's gain and drive them into a recess made by an appropriately sized Forstner. That way if they spin and shred wood the piece will still stay mounted.
Advice on checking chucking "grip" often is somewhat misleading. It might encourage you to squash your work or even splinter it if you're using a wedge hold. My recommendation is to loosen the tailstock if in use (yes!) and check for droop, which indicates the front of the jaws are not registered against the shoulder of the tenon or the bottom of the mortise. If you're not using the support, grasp the front edge and check for movement. If it moves a bit, reengage the tail in the old spot if used, loosen the chuck slightly and check it is properly bottomed, adding a bit of push from the quill if you can. Then snug the chuck back up to maintain position. It's a bit like screwing the the oil filter on your car - seat, and no more than a touch more. Loosen the tail or shake again if you have doubts. If the piece droops or moves, you have a split at the base of the tenon or the end grain of the mortise.
If you left a mortise, screw hole or center mark and a pillar, no sweat to reverse, mount and repair. If you turned any of the above away you'll want a couple of those faceplates set up as pressure chucks to remedy the situation.