Copies backups from automysqlbackup to a remote host. Retains 1 weekly and 7 daily backups per database.

copy_backups.sh

#!/usr/bin/env bash
#
# Purpose:
# Maintains 7 daily and 1 weekly database backups on a remote server.
#
# Configuration:
# Subdirectories must be created on the remote server for each database.
# (This includes status & fullschema directories if applicable.)
#
# Examples:
#
# Daily
# in:  /backups/path/daily/mydb/daily_mydb_2016-02-29_03h25m_Monday.sql.gz
# out: daily_mydb_Monday.sql.gz
#
# Weekly
# in:  /backups/path/weekly/mydb/weekly_mydb_2016-02-28_03h09m_8.sql.gz
# out: weekly_mydb.sql.gz

scpPath='user@host:path'

find '/backups/path' -type f -mmin -720 | while read file; do
  dir=$(basename $(dirname $file))
  copyFile=$(basename $file | sed 's/_[0-9]\{4\}-[0-9]\{2\}-[0-9]\{2\}_[0-9]\{2\}h[0-9]\{2\}m\(_[0-9]\+\)\?//')
  $(scp $file "$scpPath/$dir/$copyFile")
done

From what I can see, you now just need to specify a script in the POSTBACKUP line in /etc/default/automysqlbackup for copying/transferring the generated backups off-server.