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I think he is asking about a valve face grinder not a seat grinder but in any case;
New arbors are available for the popular brands including K O Lee of seat cutters/grinders. If you get one make sure it has the stone dresser with it (seat or valve grinder).
With a good arbor, the correct insert for doing Model A valves and the correct angle on the stone no matter the age of the unit I would think it should be self centering even with some wear in the stone holder, as long as you try to keep everything in a straight line.