How do I control order/arrangement of certain columns in a resultset?
You could create a new ordering table with sort order and link that to your original table. Then sort it by the sort order. 
Like this:

DECLARE @SortTable TABLE (LastName nvarchar(50), SortOrder int)

INSERT INTO @SortTable 
VALUES        ('Carson', 1)
            , ('Vargas', 2)
            , ('Ansman-Wolfe', 3)
            , ('Pak', 4)
            , ('Reiter', 5)
            , ('Varkey Chudukatil', 6)
            , ('Blythe', 7)
            , ('Mitchell', 8)

SELECT      YT.*
FROM        YourTable     AS YT
INNER JOIN  @SortTable    AS ST
    ON      ST.LastName   = YT.LastName
ORDER BY    ST.SortOrder


I used a table variable, but of course you can also use a normal table that you add in your database. Make sure you add all the possible values for lastname, otherwise you would miss out rows.