Merging list valued style options

Question

As shown in Difference between ParentList and Inherited we can use ParentList to nicely merge additional rules.

It seems to work nicely when it comes to inheriting between 'objects' like: $FrontEnd, $FrontEndSession, _StyleSheet, _Notebook(Object), _Cell(Object) etc.

I failed to make it work for StyleData[style] and StyleData[style, env] pair.

Here is an example:

CreateDocument[
  { Cell[BoxData@"", "Input"] }
 , StyleKeyMapping -> {ParentList, "&" -> "WolframAlphaShort"}
 , StyleDefinitions -> Notebook[
     { Cell[StyleData[StyleDefinitions -> "Default.nb"]]
     , Cell[StyleData["Input", "Working"]
       , StyleKeyMapping -> {ParentList, "Tab" -> "WolframAlphaShort"}         
       ]
     }
   ]
 ]

By default when you hit =, in an empty Input cell, it will be converted to a WolframAlphaShort cell.

I wanted to add & and Tab to do the same. The former explicitly in a notebook and the latter via stylesheet.

They both work but the original = does not anymore.

This means the Notebook's spec correctly merged stylesheet's spec but the stylesheet resolution failed to merge spec from Default.nb.

Should it happen? Is there any way to proceed without explicitly including parent spec?

At the end I want all &, Tab and = to produce WAShort cell.

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related:

Updating styles which are based on styles changed in private stylesheet