John,
If the problems are superficial, how about using a cup stone and grinder? I've repaired or been involved with repairs on about a dozen anvils and we've ground the face this way with much success. If you have to make welding repairs, I've used Rob Gunther's process - grind dents etc. down to clean metal, pre-heat anvil to 350d, weld w/ Stoody 2110 to base wrought iron if chip is to that depth, and 1105 if only into plate, grind smooth, re-heat to 350d, pack in ashes or vermiculite and slow cool. Sounds complicated but we've not had one failure. The rods used are not the hardest but most closely duplicate the old tool steel plate on older anvils in color and hardness. Either way, good luck.