I am trying to put some distance between making a simple backup and
purging the persistent store. Most of the time, one can make a little backup
and not even think about re-doing persistence.

I'm glad to learn there are other ways to go about re-doing persistence, but
I don't have to do that very often. So here's my take on knoppix-data.img,
but I consider this somewhat a distraction from the thread itself.

To purge a failed knoppix-data.img, it must be un-mounted first, then deleted.

One way to achieve this is to launch another working linux system, such as your
LiveCD and to delete the knoppix-data.img on an inert LiveUSB.

The cheatcode 'noimage' used in launching a LiveUSB must keep its knoppix-data.img
from being mounted, allowing one to delete it by means of the LiveUSB, without
recourse to another linux system for this purpose. I've not used it, but I can
(now) appreciate its usefulness.

In either case, the purged LiveUSB should provide the opportunity to (re)establish
a persistent file at each boot, until such time as one has in fact been
established. However, re-establishing persistence in this way purges ALL
changes inherent in the purged knoppix-data.img, both personal material and
other material not contained in home/, root/, etc/ and syslinux.cfg.

The personal backup will re-instate only the personal material. Other material
must be additionally re-constituted. The original backup program cited earlier
backs up ALL of KNOPPIX-DATA, not just the personal material if that is desired.
The storage overhead for this is considerably more, and to my mind not as efficient
a use of resources as this later 'personal version'.

So long as the LiveUSB seems to be properly functioning, there is no need to
purge-and-replace knoppix-data.img. Personal backups may be performed over and over
without recourse to purging and re-establishing persistence so long as
the OS seems to be performing as it should.