Column Names Change by Month, which throws off PowerQuery. How do I handle this?

One way to approach this is to unpivot the columns that can change (i.e. unpivot other columns selecting the columns that won't change), do whatever other filtering/transforming you need (if any), and pivot at the end if you really need to (unpivoted months are almost always easier to work with in the model though).

Here's a simple example that shouldn't break if you add or subtract months to the starting table.

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WMlTSUUoE4gogzlSK1YlWMgKykoC4EoizwCLGQFYyEFcBcbZSbCwA", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [ID = _t, Aug = _t, Sep = _t, Oct = _t]),
    #"Unpivoted Other Columns" = Table.UnpivotOtherColumns(Source, {"ID"}, "Attribute", "Value"),
    #"Uppercased Text" = Table.TransformColumns(#"Unpivoted Other Columns",{{"Value", Text.Upper, type text}}),
    #"Pivoted Column" = Table.Pivot(#"Uppercased Text", List.Distinct(#"Uppercased Text"[Attribute]), "Attribute", "Value")
in
    #"Pivoted Column"