So compressing the tar.gz itself probably isn't going to be much help, since you're trying to recompress already compressed data :)
There are other tools you can use that provide better compression ratios than gzip
, but at a cost of (sometimes ludicrously) increased compression/decompression time.
Someone over on AskUbuntu already put together a phenomenal answer as to exact numbers on what the better compression methods are, but you couldn't go wrong by trying p7zip
(available from most package managers)
Remember though that video files in most cases are already compressed, so the gains by using a much better algorithm probably won't be great.