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My thanks and congratulations in particular to Ruud van der Weele and Paul Beuk, who got the correct genus right off. Somehow this percolated down to nearer home and the Natal Museum, from where Burgert Muller wrote:
"...this fly photo ended up at the museum via Diptera.info. for identification. It is a Lauxaniid, belonging to the genus Pachycerina (Identification by Dr. Ray Miller) A paper on them can be viewed at
https://www.dropbox.com/s/scmxppirfhpsvfz/afin2E0502E0207.pdf?dl=0
Unfortunately the abdomen is obscured, so getting it to species will be nearly impossible."

That article certainly settles the matter, I reckon.

My thanks to all who contributed.