Why use zip. Use a native unix format such as tar.
Here is how you can perform a backup, using tar and don't need to have the actual tar file produced:
tar -C / -cf - /home /usr /srv /bin /sbin | ssh user@host tar -C <backup_dir> -xvf -
This will create the subdirectories that you don't want but the -C <dir> option allows you to change the base directory to start from and restore to, which is similar to your question.
You could use cpio instead of tar.
Here is an example which copies the files to my home directory in my desktop, via ssh. While the work/list* files are listed, without the -d option, they are all created in the same directory.
ls index.html* work/list* | cpio --create -v | ssh hpmedia cpio -vi -
If you do start from a tar or cpio file, you can simply cat the archive file through the pipe.