While I still don't know why the output is printing twice, this is the script I was ultimately trying to come up with and it works. That's all I really needed. This thread was simply a result of the odd, mostly unrelated output I was seeing.

#!/usr/bin/perl

use strict;
use warnings;
use Lingua::JA::Numbers;

my $len = $ARGV[0];
my (@numList, @rom, @kana, @kanji, %randList);
open(OUTFILE, '>', 'converted.csv');
binmode OUTFILE, ":utf8";

while ((scalar(keys %randList)) != $ARGV[1]){
    $randList{int (rand (1 . 0 x (int (rand $len))))} = 1;
}

@numList = keys %randList;

for my $num (@numList){
    my $jaRom = Lingua::JA::Numbers->new($num, {style=>'romaji'});
    my $jaKana = Lingua::JA::Numbers->new($num, {style=>'hiragana'});
    my $jaKanji = Lingua::JA::Numbers->new($num, {style=>'kanji'});
    push @rom, $jaRom;
    push @kana, $jaKana;
    push @kanji, $jaKanji;
}

my (@hyphens, @noHyphens);
for my $strg (@rom){
    @hyphens = Lingua::JA::Numbers::to_string($strg);
    foreach my $val (@hyphens){
        $val =~ s/-//g;
    }
    push @noHyphens, join(' ', @hyphens);
}

@rom = @noHyphens;

for (my $i = 0; $i < (scalar @numList); ++$i){
    print OUTFILE $numList[$i] . "," . $rom[$i] . "," . $kana[$i] .","
+ . $kanji[$i] . "\n";
}

close OUTFILE;
[download]

If we can figure out the cause of the output I'll be happy but it isn't really a pressing matter.