Rather long for a comment:

I think the OP's goals are going to be hard to achieve.  `GoldenRatio` is embedded in the system in ways I don't know.  Here is some examples of the embedding that come from an internal [`Trace`](http://reference.wolfram.com/language/ref/Trace.html) of `FunctionExpand@GoldenRation`:

    GoldenRatio /. SimplifyDump`PositiveRules
    SimplifyDump`$FSTab /@ %
    (*
      {901}
      {GoldenRatio :> 1/2 (1 + Sqrt[5])}
    *)

Some of the OP's goals can be handled programmatically.  For instance:

    ClearAll[OneThird];
    SetAttributes[OneThird, {Constant}];
    N[OneThird, p_: MachinePrecision] := N[1/3, p];
    
    OneThird // N[#, 22] &
    (*  0.3333333333333333333333  *)
    
However, automatic conversion to its numerical value does not happen for `OneThird` as it does for `GoldenRatio`:

    3. OneThird
    3. GoldenRatio
    (*
      3. OneThird
      4.8541
    *)

Maybe someone else will know how to do it.  An internal trace reveals nothing.