Need Help: Re-structuring table and creating columns based on rows in Query Editor or Dax

It's not super simple, but List.Generate might be faster than what you've tried.

Example:

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WSs7JTM0rcVTSUTLUN9Q3MjAyADJ9lWJ1kKWMEFKeaFLGCCkFJCkn3AYiSRli0WWEkMKhywjNGc6odvkrxcYCAA==", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [people_id = _t, el_actual_date = _t, program_status = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"people_id", type text}, {"el_actual_date", type date}, {"program_status", type text}}),
    #"Grouped Rows" = Table.Group(#"Changed Type", {"people_id"}, {{"SubTable",
        (A) => Table.Skip(Table.FromRecords(
            List.Generate(
                () => [t = [people_id = null, el_actual_date = null, program_status = null],
                       i = 0, j = 0, d = #date(1900,1,1)],
                each [i] <= Table.RowCount(A),
                each [
                        i = [i] + 1,
                        d = A{[i]}[el_actual_date],
                        j = (if d < Date.AddDays([d], 90) then [j] else [j] + 1),
                        t = A{[i]}
                    ],
                each [t] & [episode_of_care_num = [j]]
            )))
        }}),
    #"Expanded SubTable" = Table.ExpandTableColumn(#"Grouped Rows", "SubTable", {"el_actual_date", "program_status", "episode_of_care_num"}, {"el_actual_date", "program_status", "episode_of_care_num"}),
    #"Remove Non-MO" = Table.TransformColumns(#"Expanded SubTable",{{"program_status", each if _ = "M" or _ = "O" then _ else "", type text}}),
    #"Grouped Rows1" = Table.Group(#"Remove Non-MO", {"people_id", "episode_of_care_num"}, {{"eoc_start_date", each List.Min([el_actual_date]), type date}, {"eoc_end_date", each List.Max([el_actual_date]), type date}, {"M_or_O_status", each List.Max([program_status]), type text}})
in
    #"Grouped Rows1"