How can I turn off SingleLetterItalics in PlotLabel, etc, when the Options Inspector won't do it?

I don't know if it qualifies as an answer to your question if I suggest to change the structure of the labeling in the first place. As you write it, the m is -- from the rendering point of view -- treated as a symbol, if you inclose it with quotation marks it will be treated as a string and no auto-italic is performed at all. E.g.:

PlotLabel -> "Test Label in k(\!\(\*SuperscriptBox[\(\"m\"\), \\(2\)]\))"

instead of

PlotLabel -> "Test Label in k(\!\(\*SuperscriptBox[\(m\), \(2\)]\))"

another thing you should be aware of is that you can use arbitrary expressions as labels, e.g.:

PlotLabel -> Row[{"Test Label in k(", Superscript["m", 2], ")"}]

which I find much easier to automatically create and manipulate as well as manually maintain than those cryptic strings...

If, as your comments suggest, you don't have control over how these labels are created, the following could be the solution you are after:

ListLinePlot[fakedata101, Filling -> Axis, PlotStyle -> Red, 
  FillingStyle -> Red, 
  PlotLabel -> "Test Label in k(\!\(\*SuperscriptBox[\(m\), \(2\)]\))",
  FormatType -> (Style[TraditionalForm[##],SingleLetterItalics -> False] &)
]

It's in the style sheet. Use a custom style sheet to override the default.

Format > Edit Stylesheet... then enter style name: TraditionalForm

Open Format > Option Inspector... and set SingleLetterItalics to False