One of your main problems is that the gzip format means
that you have to decompress the whole tar file in order to
get any particular one out of it.
I would expect far better performance if you gzipped the
individual files and then tarred the bundle rather than
doing it the other way. This isn't usually done because
it results in less overall compression. But it means that
any particular file can be extracted relatively easily.
Also note that you could improve performance even more by
just losing the idea of having a tar. But if you do that
then you need to be very, very careful about security else
someone will be able to access any gzipped file on your