Yes, the flat plug is pretty common, but you'll need to find a FLAPS counter man who actually needs to shave more than once a week. One with a little gray around the temples is even better. Clean the shallow groove thoroughly, maybe with a rotary wire brush in a drill motor, then paint a little brush-on Permatex sealer into the groove. Put the dished plug into the groove with the convex side out, and give it a firm tap in the center with a 3-lb. BFH. The dish will collapse slightly and seal the edge of the plug against the block.
Jerry