Is there Perl ways

Not really, as this is just a question of compression and archival. gzip doesn't do file-separation; it's just stream compression. So if you cat the existing .gz files together, as you see, you get one file back.

tar is made exclusively for putting multiple files together; have you considered taring the .gzs together? (You'd have .gz.tar instead of .tar.gz, kinda!)

Or, try .zip or .rar with a zero compression setting (as you will probably incur a size gain trying to compress the already compressed .gzs).