The first step in getting a handle on the data backup and recovery strategy is to untangle some of what has been done already. The key problem is that each backup server's volume group was partitioned into dozens of logical volumes. The result is that certain logical volumes are filling up (or are full) while others are under utilized.
The quickest solution would be to reduce a largely empty partition and resize the full one(s). That works but forces to me to guess at if enough space has been allocated or too little. It puts me in the position of having to actively manage space in the logical volumes.
A better approach would be to condense all of the logical volumes into one BIG one. The hope is that there will be enough overall free-space for the medium-term. That's the approach that I took. It meant recreating all of the backups and that took a few days.
In the process of condensing the logical volumes, I learned quite a bit about LVM at this Debian link and liked what I learned. Along the way, I had to readdress the backup scripts that were used. That'll be the topic of a later post.