Get some rest;) You'll work better for it.

You need to chop @files into chunks of 3,000, or less for the end. I'll not duplicate all the code, this is just an outline.

use List::Util qw(min);
foreach my $seq ( 0 .. $#files/3_000 ) {
    my $zip  = Archive::Zip->new();
    my $start = $seq * 3_000;
    my $end = min ( $#files, $start + 2_999 );
    foreach my $i ( $start .. $end ) {
        $zip->addFile( $files[$i], basename $files[$i] );
    }
    $zip->writeToFileNamed("test-$seq.zip");
}
[download]