Per Mayayana:
I don't know why you think the HP partition is critical.
I always delete those. It's only useful if you don't have
backed up disk images of C.

That was my knee-jerk reaction: just delete it.

But when I do that, the system boots up throwing a dialog that reads
something like "Desktop.ini not found" and there's basically an empty desktop
- so I jumped to the assumption that the HP partition contained some files
used day-to-day.

Vanguard, Paul, John, and you have given me hope.

I had thrown in the towel and just re-imaged to an old 1TB backup drive - but
now I think I will re-visit the scene with the 2TB drive.

First thing I will try is looking for Macrium's Resize-Partition option.

If that doesn't happen, I'll move on to Paul's approach and, if that does not
work out, will start looking for a partition manager that will do the job.

Seems pretty obvious that something else is going on that I am unaware of
vis-a-vis my incorrect assumption that the HP_RECOVERY partition was playing
an essential role.

The situation acts like there is a file (boot block?) somewhere that points
to Partition 0, Partition 1, Partition 2, and so-forth - and, when partitions
are moved around without changing that file, Bad Things happen.
--
Pete Cresswell