A minor update: This version of the loop may be a bit nicer (tested):

# works -- a while loop might be more efficient/elegant
MAX_BASES:
while (@base_values) {  # @base_values is consumed
    $max_bases .= $_->[1] for  # append base of each max
        reduce { $a->[0] > $b->[0] ? $a : $b }      # max in group
        map [ shift(@base_values), $_ ], @base_ord  # groups of n
        ;
    }
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