foreach ( sort {
    length $b <=> length $a
           ||
    lc $b cmp lc $a
                 } @$raw_hash_keys_ar ) {

    # do stuff;
}

# Processed as:
'All-American Residential Framing'
'Robert E. Matthews'
'Builders Assistant'
'Electric Systems'
'Colson Plumbing'
'P & L Lighting'
'Regis Co.'
'Greenways'