I did not realise this kind of hierarchy is particularly non-standard. I had assumed that having users assigned to groups would be a very common arrangement for a server with a larger number of separate users,
My impression is that you are mixing two things.
Of course it is very logical to divide users amongst groups (Human Resource, Sales, Finance or whatever is applicable in your situation).
That does not imply that the organisation within /home must be hierarchical. You can do it (and you did) and it has advantages, but it is no must.
Ceterum Censeo: you must find out why you have a more then full root partition and do something about it.