Writing Power Query (M language) functions that tailor table scope based on current row values

I re-read this and have another idea that may be easier. I created a helper column to determine which scores should be evaluated:

let
    Source = Excel.CurrentWorkbook(){[Name="Scores"]}[Content],
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"Specific Identifier", type text}, {"Score", Int64.Type}, {"Qualifier", type text}}),
    #"Added Qualified Scores" = Table.AddColumn(#"Changed Type", "Qualified Scores", each if [Qualifier] <> "Ignore" then [Score] else null),
    #"Added Outcome" = Table.AddColumn(#"Added Qualified Scores", "Outcome", each if (let group = [Specific Identifier] in
        List.Min(Table.SelectRows(#"Added Qualified Scores", each [Specific Identifier] = group) [Qualified Scores])) = [Score] then "Lowest" else "")
in
    #"Added Outcome"

Happy to help!

As an aside, GroupKind.Local can be a powerful tool if you're grouping rows based on proximity to one another - especially if values are repeated later on but should be kept separate i.e.: 

In a table like this, if the two A groups ({1,2,3} and {7,8}) should be aggregated separately, GroupKind.Local would allow you to do that. 

= Table.Group(#"Source Table", {"Group"}, {"Group Sum", each List.Sum([Value])}, GroupKind.Local)

When I re-read your post, I realized GroupKind.Local would have worked but wasn't necessary... but it's still a good tool to know about and one that someone just recently showed me so now I'm just trying to share the wealth :)